whole # Dec min roundConfidence Interval Lower Limit 7.22 7 0.22 13.18665 13Confidence Interval Upper Limit 8.78 8 0.78 46.81335 47

Mean 8.00 Hours to build a typical deckn 40 Sample sizesigma 3 Pop standard deviation

standard Error (hours)

0.9 How sure you are that pop mean is in Interval

Risk you take that pop mean in not in intervalAlpha/2 risk in lower and upper tail

Calculate Margin of Error Method 1z lowerz upperMargin of Error +/-Confidence Interval Lower LimitConfidence Interval Upper Limit

Calculate Margin of Error Method 2

Margin of Error +/-Confidence Interval Lower LimitConfidence Interval Upper LimitConclude:

Xbar Alpha = Risk Pop Mean Not In Interval8 Err:502

8.01 Err:5028.02 Err:5028.03 Err:5028.04 Err:5028.05 Err:5028.06 Err:5028.07 Err:5028.08 Err:5028.09 Err:502

8.1 Err:502

The Solid Construction Company constructs decks for residential homes. They send out two person teams to build decks. The company conducts a sample of 40 jobs and calculates a mean completion rate

of 8 hours to build a typical deck. The standard deviation for the population is known to be equal to 3 hours (from past data).

Standard Error (Standard Deviation of Distribution of Xbar)

Confidence Level =orConfidence Coefficient =

Alpha =Significance Level =orLevel of Significance =

CONFIDENCE function calculates the Margin of error. It has three arguments: 1) alpha = alpha, 2) standard deviation = sigma, 3) size = sample size.

8.0

8.1

8.2

8.4

8.5

8.6

8.7

8.8

9.0

9.1

9.2

9.3

9.4

9.6

9.7

9.8

9.9

10.0

10.2

10.3

10.4

10.5

10.6

10.8

10.9

11.0

11.1

11.2

11.4

11.5

11.6

11.7

11.8

12.0

12.1

12.2

00.10.20.30.40.50.60.70.80.9

1

Confidence IntervalHours to build a typical deck = 8

Confidence Level = 90.00%Alpha = Significance Level (Risk) =0.00%

Sample Size = 40Standard Error = 0.000 Margin of Error = 0.000

Confidence Interval = 90.00% = P(0.00<=x<=0.00)Alpha = Risk Pop Mean Not In Interval

Xbar

8.11 Err:5028.12 Err:5028.13 Err:5028.14 Err:5028.15 Err:5028.16 Err:5028.17 Err:5028.18 Err:5028.19 Err:502

8.2 Err:5028.21 Err:5028.22 Err:5028.23 Err:5028.24 Err:5028.25 Err:5028.26 Err:5028.27 Err:5028.28 Err:5028.29 Err:502

8.3 Err:5028.31 Err:5028.32 Err:5028.33 Err:5028.34 Err:5028.35 Err:5028.36 Err:5028.37 Err:5028.38 Err:5028.39 Err:502

8.4 Err:5028.41 Err:5028.42 Err:5028.43 Err:5028.44 Err:5028.45 Err:5028.46 Err:5028.47 Err:5028.48 Err:5028.49 Err:502

8.5 Err:5028.51 Err:5028.52 Err:5028.53 Err:5028.54 Err:5028.55 Err:502

8.0

8.1

8.2

8.4

8.5

8.6

8.7

8.8

9.0

9.1

9.2

9.3

9.4

9.6

9.7

9.8

9.9

10.0

10.2

10.3

10.4

10.5

10.6

10.8

10.9

11.0

11.1

11.2

11.4

11.5

11.6

11.7

11.8

12.0

12.1

12.2

00.10.20.30.40.50.60.70.80.9

1

Confidence IntervalHours to build a typical deck = 8

Confidence Level = 90.00%Alpha = Significance Level (Risk) =0.00%

Sample Size = 40Standard Error = 0.000 Margin of Error = 0.000

Confidence Interval = 90.00% = P(0.00<=x<=0.00)Alpha = Risk Pop Mean Not In Interval

Xbar

8.56 Err:5028.57 Err:5028.58 Err:5028.59 Err:502

8.6 Err:5028.61 Err:5028.62 Err:5028.63 Err:5028.64 Err:5028.65 Err:5028.66 Err:5028.67 Err:5028.68 Err:5028.69 Err:502

8.7 Err:5028.71 Err:5028.72 Err:5028.73 Err:5028.74 Err:5028.75 Err:5028.76 Err:5028.77 Err:5028.78 Err:5028.79 Err:502

8.8 Err:5028.81 Err:5028.82 Err:5028.83 Err:5028.84 Err:5028.85 Err:5028.86 Err:5028.87 Err:5028.88 Err:5028.89 Err:502

8.9 Err:5028.91 Err:5028.92 Err:5028.93 Err:5028.94 Err:5028.95 Err:5028.96 Err:5028.97 Err:5028.98 Err:5028.99 Err:502

9 Err:502

9.01 Err:5029.02 Err:5029.03 Err:5029.04 Err:5029.05 Err:5029.06 Err:5029.07 Err:5029.08 Err:5029.09 Err:502

9.1 Err:5029.11 Err:5029.12 Err:5029.13 Err:5029.14 Err:5029.15 Err:5029.16 Err:5029.17 Err:5029.18 Err:5029.19 Err:502

9.2 Err:5029.21 Err:5029.22 Err:5029.23 Err:5029.24 Err:5029.25 Err:5029.26 Err:5029.27 Err:5029.28 Err:5029.29 Err:502

9.3 Err:5029.31 Err:5029.32 Err:5029.33 Err:5029.34 Err:5029.35 Err:5029.36 Err:5029.37 Err:5029.38 Err:5029.39 Err:502

9.4 Err:5029.41 Err:5029.42 Err:5029.43 Err:5029.44 Err:5029.45 Err:502

9.46 Err:5029.47 Err:5029.48 Err:5029.49 Err:502

9.5 Err:5029.51 Err:5029.52 Err:5029.53 Err:5029.54 Err:5029.55 Err:5029.56 Err:5029.57 Err:5029.58 Err:5029.59 Err:502

9.6 Err:5029.61 Err:5029.62 Err:5029.63 Err:5029.64 Err:5029.65 Err:5029.66 Err:5029.67 Err:5029.68 Err:5029.69 Err:502

9.7 Err:5029.71 Err:5029.72 Err:5029.73 Err:5029.74 Err:5029.75 Err:5029.76 Err:5029.77 Err:5029.78 Err:5029.79 Err:502

9.8 Err:5029.81 Err:5029.82 Err:5029.83 Err:5029.84 Err:5029.85 Err:5029.86 Err:5029.87 Err:5029.88 Err:5029.89 Err:502

9.9 Err:502

9.91 Err:5029.92 Err:5029.93 Err:5029.94 Err:5029.95 Err:5029.96 Err:5029.97 Err:5029.98 Err:5029.99 Err:502

10 Err:50210.01 Err:50210.02 Err:50210.03 Err:50210.04 Err:50210.05 Err:50210.06 Err:50210.07 Err:50210.08 Err:50210.09 Err:502

10.1 Err:50210.11 Err:50210.12 Err:50210.13 Err:50210.14 Err:50210.15 Err:50210.16 Err:50210.17 Err:50210.18 Err:50210.19 Err:502

10.2 Err:50210.21 Err:50210.22 Err:50210.23 Err:50210.24 Err:50210.25 Err:50210.26 Err:50210.27 Err:50210.28 Err:50210.29 Err:502

10.3 Err:50210.31 Err:50210.32 Err:50210.33 Err:50210.34 Err:50210.35 Err:502

10.36 Err:50210.37 Err:50210.38 Err:50210.39 Err:502

10.4 Err:50210.41 Err:50210.42 Err:50210.43 Err:50210.44 Err:50210.45 Err:50210.46 Err:50210.47 Err:50210.48 Err:50210.49 Err:502

10.5 Err:50210.51 Err:50210.52 Err:50210.53 Err:50210.54 Err:50210.55 Err:50210.56 Err:50210.57 Err:50210.58 Err:50210.59 Err:502

10.6 Err:50210.61 Err:50210.62 Err:50210.63 Err:50210.64 Err:50210.65 Err:50210.66 Err:50210.67 Err:50210.68 Err:50210.69 Err:502

10.7 Err:50210.71 Err:50210.72 Err:50210.73 Err:50210.74 Err:50210.75 Err:50210.76 Err:50210.77 Err:50210.78 Err:50210.79 Err:502

10.8 Err:502

10.81 Err:50210.82 Err:50210.83 Err:50210.84 Err:50210.85 Err:50210.86 Err:50210.87 Err:50210.88 Err:50210.89 Err:502

10.9 Err:50210.91 Err:50210.92 Err:50210.93 Err:50210.94 Err:50210.95 Err:50210.96 Err:50210.97 Err:50210.98 Err:50210.99 Err:502

11 Err:50211.01 Err:50211.02 Err:50211.03 Err:50211.04 Err:50211.05 Err:50211.06 Err:50211.07 Err:50211.08 Err:50211.09 Err:502

11.1 Err:50211.11 Err:50211.12 Err:50211.13 Err:50211.14 Err:50211.15 Err:50211.16 Err:50211.17 Err:50211.18 Err:50211.19 Err:502

11.2 Err:50211.21 Err:50211.22 Err:50211.23 Err:50211.24 Err:50211.25 Err:502

11.26 Err:50211.27 Err:50211.28 Err:50211.29 Err:502

11.3 Err:50211.31 Err:50211.32 Err:50211.33 Err:50211.34 Err:50211.35 Err:50211.36 Err:50211.37 Err:50211.38 Err:50211.39 Err:502

11.4 Err:50211.41 Err:50211.42 Err:50211.43 Err:50211.44 Err:50211.45 Err:50211.46 Err:50211.47 Err:50211.48 Err:50211.49 Err:502

11.5 Err:50211.51 Err:50211.52 Err:50211.53 Err:50211.54 Err:50211.55 Err:50211.56 Err:50211.57 Err:50211.58 Err:50211.59 Err:502

11.6 Err:50211.61 Err:50211.62 Err:50211.63 Err:50211.64 Err:50211.65 Err:50211.66 Err:50211.67 Err:50211.68 Err:50211.69 Err:502

11.7 Err:502

11.71 Err:50211.72 Err:50211.73 Err:50211.74 Err:50211.75 Err:50211.76 Err:50211.77 Err:50211.78 Err:50211.79 Err:502

11.8 Err:50211.81 Err:50211.82 Err:50211.83 Err:50211.84 Err:50211.85 Err:50211.86 Err:50211.87 Err:50211.88 Err:50211.89 Err:502

11.9 Err:50211.91 Err:50211.92 Err:50211.93 Err:50211.94 Err:50211.95 Err:50211.96 Err:50211.97 Err:50211.98 Err:50211.99 Err:502

12 Err:50212.01 Err:50212.02 Err:50212.03 Err:50212.04 Err:50212.05 Err:50212.06 Err:50212.07 Err:50212.08 Err:50212.09 Err:502

12.1 Err:50212.11 Err:50212.12 Err:50212.13 Err:50212.14 Err:50212.15 Err:502

12.16 Err:50212.17 Err:50212.18 Err:50212.19 Err:502

12.2 Err:502

8 40 3

=B4/SQRT(B3)

0.9

=1-B6 =B7/2 =NORMSINV(B8) =NORMSINV(1-B8) #ADDIN? =B11*B5 =B2-B12 =B2+B12

=CONFIDENCE(B7,B4,B3) =B2-B16 =B2+B16

Confidence Interval = 90.00% = P(0.00<=x<=0.00)

Standard Error = 0.000 Margin of Error = 0.000

Mean 8.00 Hours to build a typical deckn 40 Sample sizesigma 3 Pop standard deviation

standard Error (hours) 0.474341649

0.9 How sure you are that pop mean is in Interval

0.1 Risk you take that pop mean in not in intervalAlpha/2 0.05 risk in lower and upper tail

Calculate Margin of Error Method 1z lower -1.64485363z upper 1.644853627Margin of Error +/- 0.780222582Confidence Interval Lower Limit 7.21978 7 hours and 13 minutesConfidence Interval Upper Limit 8.78022 8 hours and 47 minutes

Calculate Margin of Error Method 2

Margin of Error +/- 0.780222582Confidence Interval Lower Limit 7.21978Confidence Interval Upper Limit 8.78022Conclude:

Xbar Alpha = Risk Pop Mean Not In Interval6.102633404 0.0002821388887943916.112633404 0.0003068946856341686.122633404 0.0003336743051030716.132633404 0.0003626295087333486.142633404 0.000393922238134308

The Solid Construction Company constructs decks for residential homes. They send out two person teams to build decks. The company conducts a sample of 40 jobs and calculates a mean completion rate

of 8 hours to build a typical deck. The standard deviation for the population is known to be equal to 3 hours (from past data).

Standard Error (Standard Deviation of Distribution of Xbar)

Confidence Level =orConfidence Coefficient =

Alpha =Significance Level =orLevel of Significance =

CONFIDENCE function calculates the Margin of error. It has three arguments: 1) alpha = alpha, 2) standard deviation = sigma, 3) size = sample size.

The limits for the 90.00% Confidence Interval are 7.22 and 8.78. It is reasonable to assume that the population mean for 'Hours to build a typical deck' is within our interval (given a 10.00% risk). We are

90.00% sure that the population mean is between these limits. However, we do take a 10.00% risk that the Population means is not within our interval. If our population distribution is normally distributed or

our n is large enough, if we were to construct 100 similar intervals, we would expect to find our population mean in 90 of them, and 10 would not contain the population mean.

6.1

6.2

6.3

6.5

6.6

6.7

6.8

6.9

7.1

7.2

7.3

7.4

7.5

7.7

7.8

7.9

8.0

8.1

8.3

8.4

8.5

8.6

8.7

8.9

9.0

9.1

9.2

9.3

9.5

9.6

9.7

9.8

9.9

10.1

10.2

10.3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Confidence IntervalHours to build a typical deck = 8

Confidence Level = 90.00%Alpha = Significance Level (Risk) =10.00%

Sample Size = 40Standard Error = 0.474

Margin of Error = 0.780

Confidence Interval = 90.00% = P(7.22<=x<=8.78)Alpha = Risk Pop Mean Not In Interval

Xbar

6.152633404 0.0004277251981385046.162633404 0.0004642224654724546.172633404 0.0005036101234626366.182633404 0.0005460969232470646.192633404 0.0005919049719170596.202633404 0.0006412704479627486.212633404 0.0006944443443389286.222633404 0.0007516932394051456.232633404 0.0008133000959248276.242633404 0.0008795650882328196.252633404 0.0009508064575985716.262633404 0.001027361395723256.272633404 0.001109586956212986.282633404 0.001197860993767126.292633404 0.001292583130709846.302633404 0.001394175750374966.312633404 0.001503085016728266.322633404 0.001619781919477716.332633404 0.001744763343780756.342633404 0.001878553163508576.352633404 0.00202170335687026.362633404 0.002174795143034386.372633404 0.002338440138214926.382633404 0.002513281529504746.392633404 0.002699995264556916.402633404 0.002899291255015716.412633404 0.003111914591399786.422633404 0.003338646766930836.432633404 0.003580306907587166.442633404 0.003837753005441216.452633404 0.004111883152114466.462633404 0.004403636768953196.472633404 0.004713995830293986.482633404 0.005043986075949596.492633404 0.005394678208805956.502633404 0.005767189073177656.512633404 0.00616268280932586.522633404 0.006582371979298536.532633404 0.007027518659011026.542633404 0.007499435491240776.552633404 0.007999486693976226.562633404 0.008529089018322216.572633404 0.009089712649937966.582633404 0.009682882047761196.592633404 0.0103101767135588

6.1

6.2

6.3

6.5

6.6

6.7

6.8

6.9

7.1

7.2

7.3

7.4

7.5

7.7

7.8

7.9

8.0

8.1

8.3

8.4

8.5

8.6

8.7

8.9

9.0

9.1

9.2

9.3

9.5

9.6

9.7

9.8

9.9

10.1

10.2

10.3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Confidence IntervalHours to build a typical deck = 8

Confidence Level = 90.00%Alpha = Significance Level (Risk) =10.00%

Sample Size = 40Standard Error = 0.474

Margin of Error = 0.780

Confidence Interval = 90.00% = P(7.22<=x<=8.78)Alpha = Risk Pop Mean Not In Interval

Xbar

6.602633404 0.01097323188564046.612633404 0.01167373914987856.622633404 0.01241344696099776.632633404 0.01319416106693156.642633404 0.01401774482889186.652633404 0.01488611942966526.662633404 0.0158012639625366.672633404 0.01676521539314116.682633404 0.01778006838649266.692633404 0.01884797499135496.702633404 0.01997114417414466.712633404 0.02115184119452436.722633404 0.02239238681489876.732633404 0.02369515633608746.742633404 0.02506257845154396.752633404 0.02649713391262576.762633404 0.02800135399758356.772633404 0.02957781877714346.782633404 0.0312291551697966.792633404 0.03295803478018456.802633404 0.03476717151430736.812633404 0.0366593189656096.822633404 0.03863726756643586.832633404 0.04070384149977956.842633404 0.04286189536671936.852633404 0.04511431060550286.862633404 0.04746399165878456.872633404 0.0499138618861546.882633404 0.05246685921975356.892633404 0.05512593156148256.902633404 0.05789403192103846.912633404 0.06077411329482756.922633404 0.06376912328660896.932633404 0.06688199847160056.942633404 0.07011565850668076.952633404 0.0734729999902586.962633404 0.07695689007635316.972633404 0.0805701598484426.982633404 0.08431559745963986.992633404 0.08819594104686357.002633404 0.09221387142768787.012633404 0.09637200458971237.022633404 0.1006728839833667.032633404 0.1051189726302077.042633404 0.109712645059899

7.052633404 0.1144561790901927.062633404 0.1193517474653687.072633404 0.1244014093697287.082633404 0.1296071018338337.092633404 0.1349706310523027.102633404 0.1404936636330537.112633404 0.1461777177989287.122633404 0.1520241545636667.132633404 0.1580341689051657.142633404 0.1642087809599377.152633404 0.1705488272635257.162633404 0.177054952062517.172633404 0.1837275987245157.182633404 0.1905670012733197.192633404 0.197573176076847.202633404 0.2047459137163247.212633404 0.2120847710655497.222633404 0.2195890636092667.232633404 0.2272578580304017.242633404 0.2350899650957637.252633404 0.2430839328701057.262633404 0.2512380402884167.272633404 0.2595502911162057.282633404 0.2680184083273347.292633404 0.2766398289286517.302633404 0.2854116992602117.312633404 0.294330870799337.322633404 0.3033938964960517.332633404 0.3125970276667697.342633404 0.3219362114718787.352633404 0.3314070890022367.362633404 0.3410049939981017.372633404 0.3507249522228767.382633404 0.3605616815126317.392633404 0.3705095925208347.402633404 0.380562790176087.412633404 0.3907150758688787.422633404 0.4009599503817017.432633404 0.4112906175745357.442633404 0.4216999888361357.452633404 0.4321806883090397.462633404 0.4427250588941577.472633404 0.4533251690384667.482633404 0.4639728203069537.492633404 0.474659555737497

7.502633404 0.4853766689749127.512633404 0.4961152141778067.522633404 0.5068660166893537.532633404 0.5176196844604537.542633404 0.5283666202111397.552633404 0.5390970343134747.562633404 0.5498009583765237.572633404 0.5604682595113987.582633404 0.5710886552517847.592633404 0.5816517291027797.602633404 0.5921469466884127.612633404 0.6025636724657187.622633404 0.6128911869708977.632633404 0.6231187045607667.642633404 0.6332353916105267.652633404 0.643230385126737.662633404 0.6530928117323667.672633404 0.6628118069790777.682633404 0.6723765349398017.692633404 0.681776208033527.702633404 0.6910001070323187.712633404 0.7000376011996827.722633404 0.7088781685078377.732633404 0.7175114158809077.742633404 0.7259270994099637.752633404 0.7341151444853587.762633404 0.7420656657913757.772633404 0.7497689871079467.782633404 0.7572156608642217.792633404 0.7643964873888647.802633404 0.7713025338023847.812633404 0.7779251524973267.822633404 0.7842559991529287.832633404 0.7902870502318057.842633404 0.7960106199073857.852633404 0.8014193763721537.862633404 0.8065063574783167.872633404 0.8112649856642167.882633404 0.8156890821217147.892633404 0.819772880161857.902633404 0.8235110377383227.912633404 0.8268986490907227.922633404 0.8299312554719997.932633404 0.8326048549273417.942633404 0.834915911094428

7.952633404 0.8368613609979987.962633404 0.8384386218146437.972633404 0.8396455965869657.982633404 0.8404806788693527.992633404 0.8409427562909978.002633404 0.8410312130250918.012633404 0.8407459311565048.022633404 0.8400872909437268.032633404 0.8390561699742278.042633404 0.837653941215898.052633404 0.8358824699705448.062633404 0.8337441097390898.072633404 0.8312416970110158.082633404 0.8283785449944868.092633404 0.8251584363063758.102633404 0.8215856146448278.112633404 0.8176647754700238.122633404 0.8134010557217678.132633404 0.8088000226054418.142633404 0.8038676614805738.152633404 0.7986103628888928.162633404 0.7930349087612328.172633404 0.7871484578449178.182633404 0.7809585303954718.192633404 0.7744729921784098.202633404 0.7677000378287528.212633404 0.7606481736174618.222633404 0.7533261996754738.232633404 0.7457431917272658.242633404 0.7379084823868768.252633404 0.7298316420702628.262633404 0.7215224595784168.272633404 0.7129909224062268.282633404 0.7042471968322538.292633404 0.6953016078446928.302633404 0.6861646189586458.312633404 0.6768468119794958.322633404 0.6673588667666648.332633404 0.6577115410513378.342633404 0.6479156503608398.352633404 0.637982048101318.362633404 0.627921605849098.372633404 0.6177451938998418.382633404 0.6074636621229128.392633404 0.597087821166748

8.402633404 0.5866284240593598.412633404 0.5760961482458928.422633404 0.5655015781033128.432633404 0.5548551879700488.442633404 0.5441673257261628.452633404 0.5334481969572918.462633404 0.5227078497331968.472633404 0.5119561600292378.482633404 0.5012028178166098.492633404 0.4904573138445598.502633404 0.4797289271352378.512633404 0.4690267132091818.522633404 0.4583594930568328.532633404 0.447735842868838.542633404 0.4371640845352398.552633404 0.4266522769212398.562633404 0.4162082079242958.572633404 0.4058393873152568.582633404 0.39555304036348.592633404 0.385356102243028.602633404 0.3752552132168018.612633404 0.3652567145889958.622633404 0.3553666454191748.632633404 0.34559073998538.642633404 0.3359344259828088.652633404 0.3264028234445128.662633404 0.3170007443643568.672633404 0.3077326930063268.682633404 0.298602866878298.692633404 0.2896151583490398.702633404 0.2807731568854998.712633404 0.272080151885848.722633404 0.2635391360831028.732633404 0.2551528094930078.742633404 0.2469235838787438.752633404 0.2388535877047878.762633404 0.230944671551218.772633404 0.2231984139594318.782633404 0.2156161276799778.792633404 0.2081988662925868.802633404 0.2009474311688098.812633404 0.193862378747238.822633404 0.1869440280915198.832633404 0.1801924687016498.842633404 0.173607568548923

8.852633404 0.1671889823057898.862633404 0.1609361597418628.872633404 0.1548483542581278.882633404 0.1489246315318848.892633404 0.1431638782456898.902633404 0.1375648108742868.912633404 0.1321259845043468.922633404 0.1268458016627018.932633404 0.1217225211296538.942633404 0.1167542667149498.952633404 0.1119390359749748.962633404 0.1072747088507838.972633404 0.102759056207658.982633404 0.09838974825790418.992633404 0.09416436284993539.002633404 0.09008039360738359.012633404 0.08613525790364079.022633404 0.0823263046579499.032633404 0.07865082194050119.042633404 0.07510604437508399.052633404 0.07168916032892449.062633404 0.06839731888050419.072633404 0.0652276365571959.082633404 0.06217720383564179.092633404 0.05924309139885499.102633404 0.05642235614500079.112633404 0.05371204694385729.122633404 0.05110921013786549.132633404 0.04861089478561989.142633404 0.04621415764653389.152633404 0.04391606790625529.162633404 0.04171371164321879.172633404 0.03960419603748559.182633404 0.03758465332374679.192633404 0.0356522444910479.202633404 0.03380416273242489.212633404 0.03203763664826069.222633404 0.03034993320767819.232633404 0.02873836047284789.242633404 0.02720027009151349.252633404 0.02573305956347819.262633404 0.0243341742871759.272633404 0.02300110939277819.282633404 0.02173141136861549.292633404 0.0205226794878997

9.302633404 0.01937256704301829.312633404 0.01827878239480119.322633404 0.01723908984434229.332633404 0.01625131033505389.342633404 0.01531332199272229.352633404 0.01442306051137789.362633404 0.01357851939281339.372633404 0.01277775004757669.382633404 0.01201886176522769.392633404 0.011300021561599.402633404 0.01061945391064539.412633404 0.009975440368612349.422633404 0.00936631909763089.432633404 0.008790484296324449.442633404 0.008246385544362229.452633404 0.007732527067960029.462633404 0.00724746693307989.472633404 0.006789816172883449.482633404 0.006358237855789759.492633404 0.005951446100265059.502633404 0.005568205042252219.512633404 0.005207327760911949.522633404 0.004867675168113389.532633404 0.00454815486687169.542633404 0.004247719983687129.552633404 0.00396536797949899.562633404 0.003700139443718579.572633404 0.003451116875570219.582633404 0.003217423456718259.592633404 0.002998221818927039.602633404 0.002792712810259049.612633404 0.002600134263086719.622633404 0.002419759766964979.632633404 0.002250897449188549.642633404 0.002092888765641369.652633404 0.00194510730433399.662633404 0.001806957603819599.672633404 0.001677873988483639.682633404 0.001557319422506629.692633404 0.001444784384121629.702633404 0.001339785761607489.712633404 0.001241865772292469.722633404 0.001150590905681729.732633404 0.001065550891669279.742633404 0.000986357694649633

9.752633404 0.0009126445342074889.762633404 0.0008440649329339179.772633404 0.0007802917917959399.782633404 0.0007210164933719519.792633404 0.0006659480331588069.802633404 0.0006148121790568349.812633404 0.0005673506590468399.822633404 0.0005233203769876989.832633404 0.0004824926563846529.842633404 0.0004446525119063329.852633404 0.0004095979483628189.862633404 0.000377139286797419.872633404 0.0003470985172909869.882633404 0.000319308678029599.892633404 0.0002936132601430139.902633404 0.0002698656377843519.912633404 0.0002479285228874749.922633404 0.0002276734440109859.932633404 0.0002089802486530569.942633404 0.000191736628401499.952633404 0.0001758376662670669.962633404 0.0001611854055354829.972633404 0.0001476884394638129.982633404 0.0001352615211410279.992633404 0.000123825192828612

10.0026334 0.00011330543409647310.0126334 0.00010363332807076610.0226334 9.47447451140788E-0510.0326334 8.6580043264037E-0510.0426334 7.90837847639716E-0510.0526334 7.22044680284025E-0510.0626334 6.58942743966866E-0510.0726334 6.01088290400647E-0510.0826334 5.4806975400334E-0510.0926334 4.99505625523679E-0510.1026334 4.55042448975283E-0510.1126334 4.14352936105513E-0510.1226334 3.77134192786256E-0510.1326334 3.43106051879751E-0510.1426334 3.12009507302448E-0510.1526334 2.8360524418226E-0510.1626334 2.57672260178945E-0510.1726334 2.34006573212592E-0510.1826334 2.12420011020759E-0510.1926334 1.9273907813985E-05

10.2026334 1.74803896080325E-0510.2126334 1.58467212637698E-0510.2226334 1.43593476451442E-0510.2326334 1.3005797309155E-0510.2426334 1.17746019117099E-0510.2526334 1.06552210712383E-0510.2626334 9.63797236638571E-0610.2726334 8.71396615947751E-0610.2826334 7.87504495240529E-0610.2926334 7.11372699611398E-0610.3026334 6.42315388895622E-06

8 40 3

=B4/SQRT(B3)

0.9

=1-B6 =B7/2 =NORMSINV(B8) =NORMSINV(1-B8) #ADDIN? =B11*B5 =B2-B12 =B2+B12

=CONFIDENCE(B7,B4,B3) =B2-B16 =B2+B16

Confidence Interval = 90.00% = P(7.22<=x<=8.78)

Standard Error = 0.474 Margin of Error = 0.780

0.2195890636092660.2272578580304010.2350899650957630.2430839328701050.2512380402884160.2595502911162050.2680184083273340.2766398289286510.285411699260211

0.294330870799330.3033938964960510.3125970276667690.3219362114718780.3314070890022360.3410049939981010.3507249522228760.3605616815126310.370509592520834

0.380562790176080.3907150758688780.4009599503817010.4112906175745350.4216999888361350.4321806883090390.4427250588941570.4533251690384660.4639728203069530.474659555737497

0.4853766689749120.4961152141778060.5068660166893530.5176196844604530.5283666202111390.5390970343134740.5498009583765230.5604682595113980.5710886552517840.5816517291027790.5921469466884120.6025636724657180.6128911869708970.6231187045607660.633235391610526

0.643230385126730.6530928117323660.6628118069790770.672376534939801

0.681776208033520.6910001070323180.7000376011996820.7088781685078370.7175114158809070.7259270994099630.7341151444853580.7420656657913750.7497689871079460.7572156608642210.7643964873888640.7713025338023840.7779251524973260.7842559991529280.7902870502318050.7960106199073850.8014193763721530.8065063574783160.8112649856642160.815689082121714

0.819772880161850.8235110377383220.8268986490907220.8299312554719990.8326048549273410.834915911094428

0.8368613609979980.8384386218146430.8396455965869650.8404806788693520.8409427562909970.8410312130250910.8407459311565040.8400872909437260.839056169974227

0.837653941215890.8358824699705440.8337441097390890.8312416970110150.8283785449944860.8251584363063750.8215856146448270.8176647754700230.8134010557217670.8088000226054410.8038676614805730.7986103628888920.7930349087612320.7871484578449170.7809585303954710.7744729921784090.7677000378287520.7606481736174610.7533261996754730.7457431917272650.7379084823868760.7298316420702620.7215224595784160.7129909224062260.7042471968322530.6953016078446920.6861646189586450.6768468119794950.6673588667666640.6577115410513370.647915650360839

0.637982048101310.62792160584909

0.6177451938998410.6074636621229120.597087821166748

0.5866284240593590.5760961482458920.5655015781033120.5548551879700480.5441673257261620.5334481969572910.5227078497331960.5119561600292370.5012028178166090.4904573138445590.4797289271352370.4690267132091810.458359493056832

0.447735842868830.4371640845352390.4266522769212390.4162082079242950.405839387315256

0.39555304036340.38535610224302

0.3752552132168010.3652567145889950.355366645419174

0.34559073998530.3359344259828080.3264028234445120.3170007443643560.307732693006326

0.298602866878290.2896151583490390.280773156885499

0.272080151885840.2635391360831020.2551528094930070.2469235838787430.238853587704787

0.230944671551210.223198413959431

Amount Mean17.35 n Sample size18.03 sigma 5 Pop standard deviation

18.13 SE

18.46 0.95

18.6219.16 Alpha/2 risk in lower and upper tail19.81 Calculate Margin of Error Method 119.82 z lower20.18 z upper20.34 Margin of Error +/-

20.60

20.7820.99 Calculate Margin of Error Method 2

21.21 Margin of Error +/-21.43 Confidence Interval Lower Limit21.44 Confidence Interval Upper Limit21.48 Conclude:22.0322.1422.20 Xbar Alpha = Risk Pop Mean Not In Inte22.22 0 Err:50222.24 0.01 Err:50222.42 0.02 Err:50222.44 0.03 Err:50222.55 0.04 Err:50222.88 0.05 Err:50223.12 0.06 Err:50223.62 0.07 Err:50223.63 0.08 Err:50223.89 0.09 Err:50224.19 0.1 Err:502

Mean dollars spent per customer in Seattle restaurants

Standard Error (Standard Deviation of Distribution of Xbar)

Confidence Level =orConfidence Coefficient =

How sure you are that pop mean is in Interval

Alpha =Significance Level =orLevel of Significance =

Risk you take that pop mean in not in interval

Confidence Interval Lower Limit

Confidence Interval Upper Limit

CONFIDENCE function calculates the Margin of error. It has three arguments: 1) alpha = alpha, 2) standard deviation = sigma, 3) size = sample size.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

00.10.20.30.40.50.60.70.80.9

1

Confidence IntervalMean dollars spent per customer in Seattle restaurants = $0.00

Confidence Level = 95.00%Alpha = Significance Level (Risk) =0.00%

Sample Size = Standard Error = 0.000

Margin of Error = 0.000

Confidence Interval = 95.00% = P(0.00<=x<=0.00)Alpha = Risk Pop Mean Not In Interval

Xbar

24.72 0.11 Err:50225.27 0.12 Err:50226.74 0.13 Err:50227.43 0.14 Err:50227.84 0.15 Err:50228.38 0.16 Err:50228.56 0.17 Err:50229.29 0.18 Err:50230.04 0.19 Err:50230.25 0.2 Err:50230.43 0.21 Err:50230.76 0.22 Err:50232.36 0.23 Err:50232.72 0.24 Err:50234.40 0.25 Err:50237.21 0.26 Err:50239.22 0.27 Err:50242.18 0.28 Err:502

0.29 Err:5020.3 Err:502

0.31 Err:5020.32 Err:5020.33 Err:5020.34 Err:5020.35 Err:5020.36 Err:5020.37 Err:5020.38 Err:5020.39 Err:502

0.4 Err:5020.41 Err:5020.42 Err:5020.43 Err:5020.44 Err:5020.45 Err:5020.46 Err:5020.47 Err:5020.48 Err:5020.49 Err:502

0.5 Err:5020.51 Err:5020.52 Err:5020.53 Err:5020.54 Err:5020.55 Err:5020.56 Err:5020.57 Err:5020.58 Err:502

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

00.10.20.30.40.50.60.70.80.9

1

Confidence IntervalMean dollars spent per customer in Seattle restaurants = $0.00

Confidence Level = 95.00%Alpha = Significance Level (Risk) =0.00%

Sample Size = Standard Error = 0.000

Margin of Error = 0.000

Confidence Interval = 95.00% = P(0.00<=x<=0.00)Alpha = Risk Pop Mean Not In Interval

Xbar

0.59 Err:5020.6 Err:502

0.61 Err:5020.62 Err:5020.63 Err:5020.64 Err:5020.65 Err:5020.66 Err:5020.67 Err:5020.68 Err:5020.69 Err:502

0.7 Err:5020.71 Err:5020.72 Err:5020.73 Err:5020.74 Err:5020.75 Err:5020.76 Err:5020.77 Err:5020.78 Err:5020.79 Err:502

0.8 Err:5020.81 Err:5020.82 Err:5020.83 Err:5020.84 Err:5020.85 Err:5020.86 Err:5020.87 Err:5020.88 Err:5020.89 Err:502

0.9 Err:5020.91 Err:5020.92 Err:5020.93 Err:5020.94 Err:5020.95 Err:5020.96 Err:5020.97 Err:5020.98 Err:5020.99 Err:502

1 Err:5021.01 Err:5021.02 Err:5021.03 Err:5021.04 Err:5021.05 Err:5021.06 Err:502

1.07 Err:5021.08 Err:5021.09 Err:502

1.1 Err:5021.11 Err:5021.12 Err:5021.13 Err:5021.14 Err:5021.15 Err:5021.16 Err:5021.17 Err:5021.18 Err:5021.19 Err:502

1.2 Err:5021.21 Err:5021.22 Err:5021.23 Err:5021.24 Err:5021.25 Err:5021.26 Err:5021.27 Err:5021.28 Err:5021.29 Err:502

1.3 Err:5021.31 Err:5021.32 Err:5021.33 Err:5021.34 Err:5021.35 Err:5021.36 Err:5021.37 Err:5021.38 Err:5021.39 Err:502

1.4 Err:5021.41 Err:5021.42 Err:5021.43 Err:5021.44 Err:5021.45 Err:5021.46 Err:5021.47 Err:5021.48 Err:5021.49 Err:502

1.5 Err:5021.51 Err:5021.52 Err:5021.53 Err:5021.54 Err:502

1.55 Err:5021.56 Err:5021.57 Err:5021.58 Err:5021.59 Err:502

1.6 Err:5021.61 Err:5021.62 Err:5021.63 Err:5021.64 Err:5021.65 Err:5021.66 Err:5021.67 Err:5021.68 Err:5021.69 Err:502

1.7 Err:5021.71 Err:5021.72 Err:5021.73 Err:5021.74 Err:5021.75 Err:5021.76 Err:5021.77 Err:5021.78 Err:5021.79 Err:502

1.8 Err:5021.81 Err:5021.82 Err:5021.83 Err:5021.84 Err:5021.85 Err:5021.86 Err:5021.87 Err:5021.88 Err:5021.89 Err:502

1.9 Err:5021.91 Err:5021.92 Err:5021.93 Err:5021.94 Err:5021.95 Err:5021.96 Err:5021.97 Err:5021.98 Err:5021.99 Err:502

2 Err:5022.01 Err:5022.02 Err:502

2.03 Err:5022.04 Err:5022.05 Err:5022.06 Err:5022.07 Err:5022.08 Err:5022.09 Err:502

2.1 Err:5022.11 Err:5022.12 Err:5022.13 Err:5022.14 Err:5022.15 Err:5022.16 Err:5022.17 Err:5022.18 Err:5022.19 Err:502

2.2 Err:5022.21 Err:5022.22 Err:5022.23 Err:5022.24 Err:5022.25 Err:5022.26 Err:5022.27 Err:5022.28 Err:5022.29 Err:502

2.3 Err:5022.31 Err:5022.32 Err:5022.33 Err:5022.34 Err:5022.35 Err:5022.36 Err:5022.37 Err:5022.38 Err:5022.39 Err:502

2.4 Err:5022.41 Err:5022.42 Err:5022.43 Err:5022.44 Err:5022.45 Err:5022.46 Err:5022.47 Err:5022.48 Err:5022.49 Err:502

2.5 Err:502

2.51 Err:5022.52 Err:5022.53 Err:5022.54 Err:5022.55 Err:5022.56 Err:5022.57 Err:5022.58 Err:5022.59 Err:502

2.6 Err:5022.61 Err:5022.62 Err:5022.63 Err:5022.64 Err:5022.65 Err:5022.66 Err:5022.67 Err:5022.68 Err:5022.69 Err:502

2.7 Err:5022.71 Err:5022.72 Err:5022.73 Err:5022.74 Err:5022.75 Err:5022.76 Err:5022.77 Err:5022.78 Err:5022.79 Err:502

2.8 Err:5022.81 Err:5022.82 Err:5022.83 Err:5022.84 Err:5022.85 Err:5022.86 Err:5022.87 Err:5022.88 Err:5022.89 Err:502

2.9 Err:5022.91 Err:5022.92 Err:5022.93 Err:5022.94 Err:5022.95 Err:5022.96 Err:5022.97 Err:5022.98 Err:502

2.99 Err:5023 Err:502

3.01 Err:5023.02 Err:5023.03 Err:5023.04 Err:5023.05 Err:5023.06 Err:5023.07 Err:5023.08 Err:5023.09 Err:502

3.1 Err:5023.11 Err:5023.12 Err:5023.13 Err:5023.14 Err:5023.15 Err:5023.16 Err:5023.17 Err:5023.18 Err:5023.19 Err:502

3.2 Err:5023.21 Err:5023.22 Err:5023.23 Err:5023.24 Err:5023.25 Err:5023.26 Err:5023.27 Err:5023.28 Err:5023.29 Err:502

3.3 Err:5023.31 Err:5023.32 Err:5023.33 Err:5023.34 Err:5023.35 Err:5023.36 Err:5023.37 Err:5023.38 Err:5023.39 Err:502

3.4 Err:5023.41 Err:5023.42 Err:5023.43 Err:5023.44 Err:5023.45 Err:5023.46 Err:502

3.47 Err:5023.48 Err:5023.49 Err:502

3.5 Err:5023.51 Err:5023.52 Err:5023.53 Err:5023.54 Err:5023.55 Err:5023.56 Err:5023.57 Err:5023.58 Err:5023.59 Err:502

3.6 Err:5023.61 Err:5023.62 Err:5023.63 Err:5023.64 Err:5023.65 Err:5023.66 Err:5023.67 Err:5023.68 Err:5023.69 Err:502

3.7 Err:5023.71 Err:5023.72 Err:5023.73 Err:5023.74 Err:5023.75 Err:5023.76 Err:5023.77 Err:5023.78 Err:5023.79 Err:502

3.8 Err:5023.81 Err:5023.82 Err:5023.83 Err:5023.84 Err:5023.85 Err:5023.86 Err:5023.87 Err:5023.88 Err:5023.89 Err:502

3.9 Err:5023.91 Err:5023.92 Err:5023.93 Err:5023.94 Err:502

3.95 Err:5023.96 Err:5023.97 Err:5023.98 Err:5023.99 Err:502

4 Err:5024.01 Err:5024.02 Err:5024.03 Err:5024.04 Err:5024.05 Err:5024.06 Err:5024.07 Err:5024.08 Err:5024.09 Err:502

4.1 Err:5024.11 Err:5024.12 Err:5024.13 Err:5024.14 Err:5024.15 Err:5024.16 Err:5024.17 Err:5024.18 Err:5024.19 Err:502

4.2 Err:5024.21 Err:5024.22 Err:5024.23 Err:5024.24 Err:5024.25 Err:5024.26 Err:5024.27 Err:5024.28 Err:5024.29 Err:502

4.3 Err:5024.31 Err:5024.32 Err:5024.33 Err:5024.34 Err:5024.35 Err:5024.36 Err:5024.37 Err:5024.38 Err:5024.39 Err:502

4.4 Err:5024.41 Err:5024.42 Err:502

4.43 Err:5024.44 Err:5024.45 Err:5024.46 Err:5024.47 Err:5024.48 Err:5024.49 Err:502

4.5 Err:5024.51 Err:5024.52 Err:5024.53 Err:5024.54 Err:5024.55 Err:5024.56 Err:5024.57 Err:5024.58 Err:5024.59 Err:502

4.6 Err:5024.61 Err:5024.62 Err:5024.63 Err:5024.64 Err:5024.65 Err:5024.66 Err:5024.67 Err:5024.68 Err:5024.69 Err:502

4.7 Err:5024.71 Err:5024.72 Err:5024.73 Err:5024.74 Err:5024.75 Err:5024.76 Err:5024.77 Err:5024.78 Err:5024.79 Err:502

4.8 Err:5024.81 Err:5024.82 Err:5024.83 Err:5024.84 Err:5024.85 Err:5024.86 Err:5024.87 Err:5024.88 Err:5024.89 Err:502

4.9 Err:502

4.91 Err:5024.92 Err:5024.93 Err:5024.94 Err:5024.95 Err:5024.96 Err:5024.97 Err:5024.98 Err:5024.99 Err:502

5 Err:5025.01 Err:5025.02 Err:5025.03 Err:5025.04 Err:5025.05 Err:5025.06 Err:5025.07 Err:5025.08 Err:5025.09 Err:502

5.1 Err:5025.11 Err:5025.12 Err:5025.13 Err:5025.14 Err:5025.15 Err:5025.16 Err:5025.17 Err:5025.18 Err:5025.19 Err:502

5.2 Err:5025.21 Err:5025.22 Err:5025.23 Err:5025.24 Err:5025.25 Err:5025.26 Err:5025.27 Err:5025.28 Err:5025.29 Err:502

5.3 Err:5025.31 Err:5025.32 Err:5025.33 Err:5025.34 Err:5025.35 Err:5025.36 Err:5025.37 Err:5025.38 Err:502

5.39 Err:5025.4 Err:502

5.41 Err:5025.42 Err:5025.43 Err:5025.44 Err:5025.45 Err:5025.46 Err:5025.47 Err:5025.48 Err:5025.49 Err:502

5.5 Err:5025.51 Err:5025.52 Err:5025.53 Err:5025.54 Err:5025.55 Err:5025.56 Err:5025.57 Err:5025.58 Err:5025.59 Err:502

5.6 Err:5025.61 Err:5025.62 Err:5025.63 Err:5025.64 Err:5025.65 Err:5025.66 Err:5025.67 Err:5025.68 Err:5025.69 Err:502

5.7 Err:5025.71 Err:5025.72 Err:502

=AVERAGE(A2:A50) =COUNT(A2:A50) 5

=D3/SQRT(D2)

0.95

=1-D5 =D6/2 =NORMSINV(D7) =NORMSINV(1-D7) =NORMSINV(D5/2+0.5) =D10*D4

=D1-D11

=D1+D11

=CONFIDENCE(D6,D3,D2) =D1-D15 =D1+D15

Confidence Interval = 95.00% = P(0.00<=x<=0.00)Err:502

Alpha = Significance Level (Risk) =0.00%Sample Size = Standard Error = 0.000 Margin of Error = 0.000

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00.10.20.30.40.50.60.70.80.9

1

Confidence IntervalMean dollars spent per customer in Seattle restaurants = $0.00

Confidence Level = 95.00%Alpha = Significance Level (Risk) =0.00%

Sample Size = Standard Error = 0.000 Margin of Error = 0.000

Confidence Interval = 95.00% = P(0.00<=x<=0.00)Alpha = Risk Pop Mean Not In Interval

Xbar

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00.10.20.30.40.50.60.70.80.9

1

Confidence IntervalMean dollars spent per customer in Seattle restaurants = $0.00

Confidence Level = 95.00%Alpha = Significance Level (Risk) =0.00%

Sample Size = Standard Error = 0.000 Margin of Error = 0.000

Confidence Interval = 95.00% = P(0.00<=x<=0.00)Alpha = Risk Pop Mean Not In Interval

Xbar

Amount Mean 24.8017.35 n 49.00 Sample size18.03 sigma 5 Pop standard deviation

18.13 SE 0.714285714

18.46 0.95

18.62 0.0519.16 Alpha/2 0.025 risk in lower and upper tail19.81 Calculate Margin of Error Method 119.82 z lower -1.9599639820.18 z upper 1.959963985 1.9599639845400520.34 Margin of Error +/- 1.399974275

20.60 23.40

20.78 26.2020.99 Calculate Margin of Error Method 2

21.21 Margin of Error +/- 1.39997427521.43 Confidence Interval Lower Lim 23.4000321.44 Confidence Interval Upper Lim 26.1999721.48 Conclude:

22.0322.1422.20 Xbar Alpha = Risk Pop Mean Not In Inte22.22 21.94285714 0.00018736231607083922.24 21.95285714 0.00019813453336030522.42 21.96285714 0.0002094850258980722.44 21.97285714 0.00022144234482984222.55 21.98285714 0.000234036306985785

Mean dollars spent per customer in Seattle restaurants

Standard Error (Standard Deviation of Distribution of Xbar)

Confidence Level =orConfidence Coefficient =

How sure you are that pop mean is in Interval

Alpha =Significance Level =orLevel of Significance =

Risk you take that pop mean in not in interval

Confidence Interval Lower Limit

Confidence Interval Upper Limit

CONFIDENCE function calculates the Margin of error. It has three arguments: 1) alpha = alpha, 2) standard deviation = sigma, 3) size = sample size.

The limits for the 95.00% Confidence Interval are 23.40 and 26.20. It is reasonable to assume that the population mean for 'Mean dollars spent per customer in Seattle restaurants' is within our interval (given a 5.00% risk). We are 95.00% sure that the population mean is between these limits. However, we do take a 5.00% risk that the Population means is not within our interval. If our population distribution is normally

distributed or our n is large enough, if we were to construct 100 similar intervals, we would expect to find our population mean in 95 of them, and 5 would not contain the population mean.

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24.2

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Confidence IntervalMean dollars spent per customer in Seattle restaurants = $24.80

Confidence Level = 95.00%Alpha = Significance Level (Risk) =5.00%

Sample Size = 49Standard Error = 0.714

Margin of Error = 1.400

Confidence Interval = 95.00% = P(23.40<=x<=26.20)Alpha = Risk Pop Mean Not In Interval

Xbar

22.88 21.99285714 0.0002472980430866123.12 22.00285714 0.00026126004737230723.62 22.01285714 0.0002759562286744423.63 22.02285714 0.0002914219629520423.89 22.03285714 0.00030769414731023724.19 22.04285714 0.00032481125551974624.72 22.05285714 0.00034281339505421725.27 22.06285714 0.00036174236566128426.74 22.07285714 0.00038164171948185427.43 22.08285714 0.00040255682273081227.84 22.09285714 0.00042453491895085828.38 22.10285714 0.00044762519384957528.56 22.11285714 0.00047187884172822329.29 22.12285714 0.000497349133508930.04 22.13285714 0.00052409148636487830.25 22.14285714 0.00055216353495690830.43 22.15285714 0.0005816252042761430.76 22.16285714 0.00061253878409216232.36 22.17285714 0.00064496900500221532.72 22.18285714 0.00067898311607526734.40 22.19285714 0.00071465096408200137.21 22.20285714 0.00075204507429905239.22 22.21285714 0.00079124073287305742.18 22.22285714 0.000832316070727055

22.23285714 0.00087535214898872522.24285714 0.00092043304591676222.25285714 0.00096764594529827222.26285714 0.0010170812262866922.27285714 0.0010688325546460622.28285714 0.0011229969753637522.29285714 0.0011796750065899822.30285714 0.0012389707348582922.31285714 0.0013009919115371822.32285714 0.0013658500504587922.33285714 0.0014336605266660922.34285714 0.0015045426762156822.35285714 0.0015786198969684122.36285714 0.0016560197502956622.37285714 0.0017368740636237822.38285714 0.0018213190337346922.39285714 0.001909495330735122.40285714 0.0020015482026018922.41285714 0.0020976275802058422.42285714 0.0021978881827101722.43285714 0.0023024896232354322.44285714 0.0024115965146760222.45285714 0.0025253785755483422.46285714 0.0026440107357448

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Confidence IntervalMean dollars spent per customer in Seattle restaurants = $24.80

Confidence Level = 95.00%Alpha = Significance Level (Risk) =5.00%

Sample Size = 49Standard Error = 0.714

Margin of Error = 1.400

Confidence Interval = 95.00% = P(23.40<=x<=26.20)Alpha = Risk Pop Mean Not In Interval

Xbar

22.47285714 0.0027676732420617122.48285714 0.0028965517633636722.49285714 0.0030308374952406622.50285714 0.0031707272640083222.51285714 0.0033164236298956522.52285714 0.0034681349892584722.53285714 0.0036260756756505422.54285714 0.0037904660595785522.55285714 0.0039615326467606922.56285714 0.0041395081747025122.57285714 0.0043246317073977622.58285714 0.0045171487279557222.59285714 0.0047173112289505422.60285714 0.0049253778002821322.61285714 0.0051416137143323222.62285714 0.0053662910081939822.63285714 0.0055996885627453922.64285714 0.0058420921783362422.65285714 0.0060937946468463322.66285714 0.0063550958198727422.67285714 0.0066263026727958822.68285714 0.0069077293644722.69285714 0.0071996972922789922.70285714 0.0075025351422933122.71285714 0.0078165789342601822.72285714 0.0081421720611543122.73285714 0.0084796653230131522.74285714 0.0088294169547767422.75285714 0.0091917926478490422.76285714 0.009567165565094722.77285714 0.0099559163489825522.78285714 0.010358433122584622.79285714 0.010775111483137922.80285714 0.011206354487874722.81285714 0.011652572631825522.82285714 0.012114183817297922.83285714 0.012591613314736122.84285714 0.013085293714664322.85285714 0.013595664870416922.86285714 0.014123173831364322.87285714 0.014668274766338522.88285714 0.015231428876969922.89285714 0.015813104300647322.90285714 0.016413776002817222.91285714 0.017033925658341322.92285714 0.017674041521637522.93285714 0.018334618285334122.94285714 0.0190161569271707

22.95285714 0.019719164544890122.96285714 0.020444154178868722.97285714 0.021191644622241422.98285714 0.02196216021828822.99285714 0.022756230644853923.00285714 0.023574390685589123.01285714 0.024417179987801423.02285714 0.025285142806728423.03285714 0.026178827736046523.04285714 0.027098787424447823.05285714 0.028045578278127823.06285714 0.029019760149043723.07285714 0.030021896008814323.08285714 0.031052551608150923.09285714 0.032112295121724323.10285714 0.033201696778388823.11285714 0.034321328476704123.12285714 0.035471763385711623.13285714 0.036653575530942723.14285714 0.037867339365657523.15285714 0.039113629327328823.16285714 0.040393019379412223.17285714 0.041706082538461323.18285714 0.043053390386672323.19285714 0.044435512569961723.20285714 0.045853016281709123.21285714 0.047306465732316923.22285714 0.048796421604765723.23285714 0.050323440496369823.24285714 0.051888074346961223.25285714 0.053490869853757623.26285714 0.05513236787319723.27285714 0.056813102810047723.28285714 0.058533601994129423.29285714 0.060294385045009523.30285714 0.062095963225067523.31285714 0.063938838781345223.32285714 0.06582350427663323.33285714 0.067750441910266723.34285714 0.069720122829142623.35285714 0.071733006429481223.36285714 0.073789539649904823.37285714 0.075890156256417123.38285714 0.078035276119905923.39285714 0.08022530448681423.40285714 0.082460631243656423.41285714 0.084741630176083223.42285714 0.0870686582232214

23.43285714 0.089442054728051723.44285714 0.091862140684604423.45285714 0.094329217982783523.46285714 0.096843568651655723.47285714 0.099405454102063423.48285714 0.10201511436944623.49285714 0.1046727673577823.50285714 0.10737860808555723.51285714 0.11013280793477323.52285714 0.1129355139038823.53285714 0.11578684786569623.54285714 0.11868690583130423.55285714 0.12163575722093823.56285714 0.12463344414292723.57285714 0.12767998068173523.58285714 0.13077535219619923.59285714 0.13391951462901523.60285714 0.13711239382859923.61285714 0.14035388488441823.62285714 0.14364385147690123.63285714 0.14698212524306623.64285714 0.15036850515896823.65285714 0.15380275694011523.66285714 0.15728461246097823.67285714 0.16081376919471823.68285714 0.16438988967426723.69285714 0.16801260097587923.70285714 0.1716814942262823.71285714 0.17539612413451523.72285714 0.17915600854960223.73285714 0.18296062804507723.74285714 0.18680942553151223.75285714 0.19070180589805423.76285714 0.19463713568404123.77285714 0.1986147427817123.78285714 0.20263391617099823.79285714 0.20669390568741623.80285714 0.21079392182394423.81285714 0.21493313556787723.82285714 0.21911067827350723.83285714 0.22332564157151323.84285714 0.22757707731587423.85285714 0.23186399756911823.86285714 0.23618537462663123.87285714 0.24054014108078123.88285714 0.24492718992548923.89285714 0.24934537470190623.90285714 0.253793509685772

23.91285714 0.25827037011699123.92285714 0.26277469247191523.93285714 0.26730517477877323.94285714 0.27186047697664123.95285714 0.27643922131827123.96285714 0.28103999281707423.97285714 0.2856613397384623.98285714 0.29030177413572723.99285714 0.29495977243057124.00285714 0.29963377603829624.01285714 0.30432219203768224.02285714 0.30902339388545224.03285714 0.31373572217518924.04285714 0.31845748544049524.05285714 0.32318696100214324.06285714 0.32792239585886424.07285714 0.33266200762138724.08285714 0.33740398548926724.09285714 0.34214649126995924.10285714 0.34688766043955924.11285714 0.35162560324453924.12285714 0.35635840584374324.13285714 0.36108413148986424.14285714 0.36580082174953624.15285714 0.37050649776110924.16285714 0.37519916152913124.17285714 0.37987679725447324.18285714 0.38453737269899424.19285714 0.38917884058355824.20285714 0.39379914001816224.21285714 0.39839619796289724.22285714 0.40296793071836224.23285714 0.40751224544413424.24285714 0.41202704170381724.25285714 0.41651021303515324.26285714 0.42095964854362124.27285714 0.42537323451789824.28285714 0.42974885606550724.29285714 0.43408439876694124.30285714 0.43837775034650324.31285714 0.44262680235804624.32285714 0.44682945188379124.33285714 0.45098360324432124.34285714 0.45508716971786824.35285714 0.45913807526692424.36285714 0.46313425627021824.37285714 0.46707366325806224.38285714 0.470954262649041

24.39285714 0.47477403848601424.40285714 0.47853099416936424.41285714 0.48222315418543524.42285714 0.48584856582806824.43285714 0.48940530091116324.44285714 0.49289145747015424.45285714 0.49630516145033324.46285714 0.49964456837991124.47285714 0.50290786502574824.48285714 0.50609327102967124.49285714 0.50919904052332124.50285714 0.51222346371948824.51285714 0.51516486847789824.52285714 0.51802162184346224.53285714 0.52079213155499924.54285714 0.52347484752248724.55285714 0.52606826327092824.56285714 0.52857091734894724.57285714 0.53098139470028124.58285714 0.53329832799635324.59285714 0.53552039892818424.60285714 0.53764633945593324.61285714 0.53967493301440424.62285714 0.54160501567291524.63285714 0.54343547724798924.64285714 0.54516526236737724.65285714 0.54679337148397324.66285714 0.54831886183827524.67285714 0.54974084836808524.68285714 0.55105850456422424.69285714 0.55227106327109424.70285714 0.55337781743101624.71285714 0.55437812077132324.72285714 0.55527138843327524.73285714 0.55605709754194324.74285714 0.5567347877162824.75285714 0.55730406151868424.76285714 0.55776458484344424.77285714 0.5581160872435224.78285714 0.55835836219524124.79285714 0.55849126730051924.80285714 0.55851472442633624.81285714 0.55842871978129824.82285714 0.55823330392913824.83285714 0.55792859173918624.84285714 0.55751476227382924.85285714 0.55699205861315224.86285714 0.556360787616984

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=AVERAGE(A2:A50) =COUNT(A2:A50) 5

=D3/SQRT(D2)

0.95

=1-D5 =D6/2 =NORMSINV(D7) =NORMSINV(1-D7) =NORMSINV(D5/2+0.5) =D10*D4

=D1-D11

=D1+D11

=CONFIDENCE(D6,D3,D2) =D1-D15 =D1+D15

Confidence Interval = 95.00% = P(23.40<=x<=26.20)

Alpha = Significance Level (Risk) =5.00%Sample Size = 49Standard Error = 0.714 Margin of Error = 1.400

The limits for the 95.00% Confidence Interval are 23.40 and 26.20. It is reasonable to assume that the population mean for 'Mean dollars spent per customer in Seattle restaurants' is within our interval (given a 5.00% risk). We are 95.00% sure that the population mean is between these limits. However, we do take a 5.00% risk that the Population means is not within our interval. If our population distribution is normally

distributed or our n is large enough, if we were to construct 100 similar intervals, we would expect to find our population mean in 95 of them, and 5 would not contain the population mean.

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Confidence IntervalMean dollars spent per customer in Seattle restaurants = $24.80

Confidence Level = 95.00%Alpha = Significance Level (Risk) =5.00%

Sample Size = 49Standard Error = 0.714 Margin of Error = 1.400

Confidence Interval = 95.00% = P(23.40<=x<=26.20)Alpha = Risk Pop Mean Not In Interval

Xbar

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Confidence IntervalMean dollars spent per customer in Seattle restaurants = $24.80

Confidence Level = 95.00%Alpha = Significance Level (Risk) =5.00%

Sample Size = 49Standard Error = 0.714 Margin of Error = 1.400

Confidence Interval = 95.00% = P(23.40<=x<=26.20)Alpha = Risk Pop Mean Not In Interval

Xbar

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0.301641426478040.2969610491021240.2922959985223980.2876478481238410.283018136566656

0.278408367141920.2738200071719210.269254487455147

0.264713201755880.2601975063382210.2557087195443690.2512481214168920.2468169533646850.2424164178722440.2380476782518420.2337118584381430.2294100428247310.2251432761419930.2209125633757450.2167188697259420.2125631206047780.2084462016734410.2043689589167410.200332198754796

0.1963366881909390.192383154994955

0.188472287920740.1846047369574450.1807811136131330.1770019912299670.1732679053299030.1695793539898640.1659367982453360.1623406625213270.158791335089589

0.155289168551020.1518344803421390.1484275532645080.1450686360359920.1417579438627250.1384956590306480.1352819315155010.1321168796101180.1290005905679280.1259331212615060.1229144988550760.1199447214898580.1170237589811420.1141515535260090.1113280204206210.1085530487860090.1058265023013080.103148219943405

0.100518016731980.09793568447894670.09540099254129770.0929136885764056

0.0904734992988360.08808013123775420.08573327149403320.0834325884961913

n 40 Sample Size 40

df =B2-1Xbar 8 Hours to build a typical deck 8

s (hours) 3 3

Standard Error =B5/SQRT(B2)

Confidence Level 0.9 Probability that Pop Parameter is in our interval 0.9

Alpha =1-B7t lower

t upper =TINV(B8,B3)Margin of Error =B10*B6

=B4-B11

=B4+B11Conclude:

The Solid Construction Company constructs decks for residential homes. They send out two person teams to build decks. The company conducts a sample of 40 jobs and calculates a mean completion rate of 8 hours to build a typical deck. The standard

deviation for the population is NOT known, but s is calculated to be 3 hours.

degrees of Freedom (loss of one value to vary because we use s)

Sample Standard Deviation point estimate for pop SD, sigma

Standard Deviation for Distribution of Sample Means

Probability that Pop Parameter is NOT in our interval (Risk)

TINV function gives you t value on upper end. It has two arguments: 1) probability = alpha = 1 - confidence Interval (if they give you alpha/2, you must multiply by 2), 2) deg_freedon = degrees of freedom = n -1

Confidence Interval Lower Limit

Confidence Interval Upper Limit

The limits for the 90.00% Confidence Interval are and . It is reasonable to assume that the population mean is within our interval (given a 10.00% risk). We are 90.00% sure that the population mean for Hours to build a

typical deck is between these limits. However, we do take a 10.00% risk that the Population means is not within our interval. If our population distribution is normally distributed or our n is large enough, if we were to construct 100 similar intervals, we would expect to find our population mean in 90 of them, and 10 would not

contain the population mean.

=B5/SQRT(B2)

=TINV(B8,B3)

The limits for the 90.00% Confidence Interval are and . It is reasonable to assume that the population mean is within our interval (given a 10.00% risk). We are 90.00% sure that the population mean for Hours to build a

typical deck is between these limits. However, we do take a 10.00% risk that the Population means is not within our interval. If our population distribution is normally distributed or our n is large enough, if we were to construct 100 similar intervals, we would expect to find our population mean in 90 of them, and 10 would not

n 40 Sample Size 40

df 39 =B2-1Xbar 8 Hours to build a typical deck 8

s (hours) 3 3

Standard Error 0.474342 =B5/SQRT(B2)

Confidence Level 0.9 Probability that Pop Parameter is in our interval 0.9

Alpha 0.1 =1-B7t lower

t upper 1.684875 =TINV(B8,B3)Margin of Error 0.799206 =B10*B6

7.200794 7 hours and 12 minutes =B4-B11

8.799206 8 hours and 48 minutes =B4+B11Conclude:

The Solid Construction Company constructs decks for residential homes. They send out two person teams to build decks. The company conducts a sample of 40 jobs and calculates a mean completion rate of 8 hours to build a typical deck. The standard

deviation for the population is NOT known, but s is calculated to be 3 hours.

degrees of Freedom (loss of one value to vary because we use s)

Sample Standard Deviation point estimate for pop SD, sigma

Standard Deviation for Distribution of Sample Means

Probability that Pop Parameter is NOT in our interval (Risk)

TINV function gives you t value on upper end. It has two arguments: 1) probability = alpha = 1 - confidence Interval (if they give you alpha/2, you must multiply by 2), 2) deg_freedon = degrees of freedom = n -1

Confidence Interval Lower Limit

Confidence Interval Upper Limit

The limits for the 90.00% Confidence Interval are 7 hours and 12 minutes and 8 hours and 48 minutes. It is reasonable to assume that the population mean is within our interval (given a 10.00% risk). We are 90.00%

sure that the population mean for Hours to build a typical deck is between these limits. However, we do take a 10.00% risk that the Population means is not within our interval. If our population distribution is normally

distributed or our n is large enough, if we were to construct 100 similar intervals, we would expect to find our population mean in 90 of them, and 10 would not contain the population mean.

=B5/SQRT(B2)

=TINV(B8,B3)

The limits for the 90.00% Confidence Interval are 7 hours and 12 minutes and 8 hours and 48 minutes. It is reasonable to assume that the population mean is within our interval (given a 10.00% risk). We are 90.00%

sure that the population mean for Hours to build a typical deck is between these limits. However, we do take a 10.00% risk that the Population means is not within our interval. If our population distribution is normally

distributed or our n is large enough, if we were to construct 100 similar intervals, we would expect to find our population mean in 90 of them, and 10 would not contain the population mean.

X bar 2409 Pagesn 10# of samples 1df =B3-B4ci = 0.95 0.95t =TINV(1-B6,B5)s 304 Pages 304Standard Error =B8/SQRT(B3)Margin of error =B9*B7

=$B$2-$B$10

=$B$2+$B$10

Printers Manufacturer, Standard Deviation of the Population not known.

lower Xbar

upper Xbar

X bar 2409 Pagesn 10# of samples 1df 1 =B3-B4ci = 0.95 0.95t 12.70620474 =TINV(1-B6,B5)s 304 Pages 304Standard Error 96.13324087 =B8/SQRT(B3)Margin of error 1221.48864 =B9*B7

1187.51136 =$B$2-$B$10

3630.48864 =$B$2+$B$10

Printers Manufacturer, Standard Deviation of the Population not known.

lower Xbar

upper Xbar

Amounts The pop. mean of = $50 48.16 The pop. mean of = $60 42.22 Sample Mean is the best estimate of the population mean = Xbar = $ 49.35 46.82 SD = s = $ 9.01 51.45 Sample size = n = 2023.78 Degrees of Freedom = df = 1941.86 Confidence Level = 95%54.86 T-Value = 2.09302437.92 "Margin of Error" Amount to add & subtract from mean = $ 4.22 52.64 Confidence limit to left = $ 53.57 48.59 Confidence limit to right = $ 45.13

50.82

46.94

61.8361.6949.1761.4651.3552.6858.8443.88

There is a 0.95 probability that the population mean will show up in the confidence interval from $45.13 to $53.57.

The pop. mean of $50 is likely to be within the confidence intervalThe pop. mean of $60 is not likely to be within the confidence interval

Amounts The pop. mean of = $50 48.16 The pop. mean of = $60 42.22 Sample Mean is the best estimate of the population mean = Xbar = $ 49.35 46.82 SD = s = $ 9.01 51.45 Sample size = n = 2023.78 Degrees of Freedom = df = 1941.86 Confidence Level = 99%54.86 T-Value = 2.86093537.92 "Margin of Error" Amount to add & subtract from mean = $ 5.77 52.64 Confidence limit to left = $ 55.11 48.59 Confidence limit to right = $ 43.58

50.82

46.94

61.8361.6949.1761.46 Amounts51.3552.68 Mean 49.34858.84 Standard Error 2.01516939343.88 Median 49.995

Mode #N/AStandard Deviation 9.0121115Sample Variance 81.21815368Kurtosis 2.258706925Skewness -0.99607984Range 38.05Minimum 23.78Maximum 61.83Sum 986.96Count 20Confidence Level(95.0%) 4.217798005

upper 53.565798lower 45.130202

There is a 0.99 probability that the population mean will show up in the confidence interval from $43.58 to $55.11.

The pop. mean of $50 is likely to be within the confidence intervalThe pop. mean of $60 is not likely to be within the confidence interval

Response Binomial Tests

Yes

Yes

Yes

YesYes n*p>5Yes n*(1-p)>5Yes n Sample sizeYes YesYes No 0

Yes P(Yes) pYes P(No)Yes Confidence Level 0.95Yes Significance Level alphaYes alpha/2Yes z upper 1.95996398454005Yes Standard Error SQRT(p*(1-p)/n)Yes Margin of errorYes Lower LimitYes Upper LimitYes Conclusion:No

NoNoNoNoNoNoNoNoNoNoNoNo

A large Seattle Coffee Company says that Excel skills are important for the 600 + employees that work in the Marketing and Accounting Department. A

sample of potential employees who said they were knowledgeable with Excel is below.

Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a

Fixed number of trials, n. - Fixed # of Identical Trials = n

Only 2 outcomes are possible on each identical trial. Success or Failure. - Each trial only results in S or F

Probability of Success = p = (π "pi"). Probability of Failure = 1-p. Probability remains the same on each

trial. - p remains the same for each trial

The trials are independent (one does not affect the next) - All events are independent

sample proportion = Point Estimate

So, since this company hires people on the spot if they know their field and they know Excel, be sure to study both in school!

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

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NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYes

YesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYes

YesYesYesYesYesYesYesYesYesYesYes

=D9*D12 =IF(D7="","",D7>5) =D13*D9 =IF(D8="","",D8>5) =COUNTA(A3:A1102) =COUNTIF($A$3:$A$1102,C10) =COUNTIF($A$3:$A$1102,C11)

=D10/$D$9 Proportion of potential employees who know Excel well =D11/$D$9 0.95 =1-D14 =D15/2 =NORMSINV(1-D16) =NORMSINV(D14/2+0.5) =SQRT(D12*D13/D9) =D18*D17 =D12-D19 =D12+D19

So, since this company hires people on the spot if they know their field and they know Excel, be sure to study both in school!

Response Binomial Tests

Yes Yes

Yes Yes

Yes Yes

Yes YesYes n*p>5 354 1Yes n*(1-p)>5 746 1Yes n 1100 Sample sizeYes Yes 354Yes No 746 1100

Yes P(Yes) 0.321818 pYes P(No) 0.678182Yes Confidence Level 0.95Yes Significance Level 0.05 alphaYes alpha/2 0.025Yes z upper 1.959964 1.95996398454005Yes Standard Error 0.014086 SQRT(p*(1-p)/n)Yes Margin of error 0.027608Yes Lower Limit 0.29421Yes Upper Limit 0.349426Yes Conclusion:

No

NoNoNoNoNoNoNoNoNoNoNo

A large Seattle Coffee Company says that Excel skills are important for the 600 + employees that work in the Marketing and Accounting Department. A

sample of potential employees who said they were knowledgeable with Excel is below.

Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a

Fixed number of trials, n. - Fixed # of Identical Trials = n

Only 2 outcomes are possible on each identical trial. Success or Failure. - Each trial only results in S or F

Probability of Success = p = (π "pi"). Probability of Failure = 1-p. Probability remains the same on each

trial. - p remains the same for each trial

The trials are independent (one does not affect the next) - All events are independent

sample proportion = Point Estimate

The 95.00% confidence interval for the proportion of potential employees who know excel well is 0.2942 to 0.3494.

So, since this company hires people on the spot if they know their field and they know Excel, be sure to study both in school!

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYes

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NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNoNo

NoNoNoNoNoYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYes

YesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYes

YesYesYesYesYesYesYesYesYesYesYesYes

=D9*D12 =IF(D7="","",D7>5) =D13*D9 =IF(D8="","",D8>5) =COUNTA(A3:A1102) =COUNTIF($A$3:$A$1102,C10) =COUNTIF($A$3:$A$1102,C11)

=D10/$D$9 Proportion of potential employees who know Excel well =D11/$D$9 0.95 =1-D14 =D15/2 =NORMSINV(1-D16) =NORMSINV(D14/2+0.5) =SQRT(D12*D13/D9) =D18*D17 =D12-D19 =D12+D19

The 95.00% confidence interval for the proportion of potential employees who know excel well is 0.2942 to 0.3494.

So, since this company hires people on the spot if they know their field and they know Excel, be sure to study both in school!

1 List Variables:x = # of successes = 414n = sample size = 600p = sample proportion = x/n = =C4/C5

2 What is the best estimation for the population proportion?

Our sample proportion is the best estimate for the population proportion ==> p =

3Level of Confidence = 0.99

=1-C12Alpha/2 = =C13/2z = =NORMSINV(1-C14)Standard Error =SQRT(C6*(1-C6)/C5)Margin of error =C16*C15

=C6-C17

=C6+C17

4 Conclusions

The margin of error is 0.00%.

Furniture Land South surveyed their customers (n = 600) to see if they liked the new line of durable foam furniture decorated in bright colors. 414 said they were excited about the new line. All the

binomial tests are met.

Determine a 99% Confidence Interval: State the level of confidence, find z, and calculate the confidence intervals.

Alpha = Risk that population proportion is not in our interval =

Xbar lower end =

Xbar upper end =

The owner can be 99.00% sure that the population proportion (% of customers excited about the new product) is between 0.00% and 0.00%.

If 100 similar intervals were constructed about 99 intervals would contain the population proportion.

1 List Variables:x = # of successes = 414n = sample size = 600p = sample proportion = x/n = 0.69 =C4/C5

2 What is the best estimation for the population proportion?

Our sample proportion is the best estimate for the population proportion ==> p = 0.69

3Level of Confidence = 0.99

0.01 =1-C12Alpha/2 = 0.005 =C13/2z = 2.575829 =NORMSINV(1-C14)Standard Error 0.018881 =SQRT(C6*(1-C6)/C5)Margin of error 0.048635 =C16*C15

0.641365 =C6-C17

0.738635 =C6+C17

4 Conclusions

The margin of error is 4.86%.

Furniture Land South surveyed their customers (n = 600) to see if they liked the new line of durable foam furniture decorated in bright colors. 414 said they were excited about the new line. All the

binomial tests are met.

Determine a 99% Confidence Interval: State the level of confidence, find z, and calculate the confidence intervals.

Alpha = Risk that population proportion is not in our interval =

Xbar lower end =

Xbar upper end =

The owner can be 99.00% sure that the population proportion (% of customers excited about the new product) is between 64.14% and 73.86%.

If 100 similar intervals were constructed about 99 intervals would contain the population proportion.

Error = $5.00 sample standard deviation = $20.00 Level of confidence = 0.99

Alpha/2 =z = =NORMSINV(1-B5)Sample size estimate = =(B6*B2/B1)^2sample size = =ROUNDUP(B7,0)

ERROR = 0.03

0.3Level of confidence = 0.95

Alpha/2 =z = =NORMSINV(1-B24)Sample size estimate = =B21*(1-B21)*(B25/B20)^2sample size = =ROUNDUP(B26,0)

Alpha = Risk that pop. Mean, mu, is not in our interval =

pbar =

Alpha = Risk that population proportion is not in our interval =

2*z snE

n p pZE

( )12

Error = $5.00 sample standard deviation = $20.00 Level of confidence = 0.99

0.01Alpha/2 = 0.005z = 2.575829 =NORMSINV(1-B5)Sample size estimate = 106.1583 =(B6*B2/B1)^2sample size = 107 =ROUNDUP(B7,0)

ERROR = 0.03

0.3Level of confidence = 0.95

0.05Alpha/2 = 0.025z = 1.959964 =NORMSINV(1-B24)Sample size estimate = 896.3404 =B21*(1-B21)*(B25/B20)^2sample size = 897 =ROUNDUP(B26,0)

Alpha = Risk that pop. Mean, mu, is not in our interval =

pbar =

Alpha = Risk that population proportion is not in our interval =

2*z snE

n p pZE

( )12