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Christian Rivero

Statistics Solution

# Problem Set 2

1. Light Bulbs problem

Four brands of light bulbs are being considered for use in the final assembly area of the Saturn

plant in Spring Hill, Tennessee. The director of purchasing asked for samples of 100 from each

manufacturer. The numbers of acceptable and unacceptable bulbs from each manufacturer are

shown below. At the .05 significance level, is there a difference in the quality of the bulbs?

Manufacturer

A B C DUnacceptable 12 8 5 11

Acceptable 88 92 95 89

Total 100 100 100 100

Answer:

Null: There is no difference in the quality of bulbsAlternative: There is difference in the quality of bulbs

Uses chi square test to test the hypothesis that there a difference in the quality of the bulbs

produced by different manufacturers.

between A and B: no

between A and C: yes

between A and D: no

between B and C: no

between B and D: no

between C and D: yes

p=213,9=0.05

213 . 0.05

P=.157 > a= 0.05 accept the null. There is no difference in the quality of the bulb.

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2. Quality control department town problem

National News Sports

Undercharge 20 10Overcharge 15 30Correct Price 200 225Total 235 265

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3. DPWH Problem

Answer:

Null Hypothesis: There is no significant relationship between the number of bidders and the

amount of winning bid on highway projects.

Alternative Hypothesis: There is a significant relationship between the number of bidders and the

amount of winning bid on highway projects.

An inverse relation has a regression equation of

y = 5.72 + 13.87/x ± 2.3707

(r = 0.58757)A straight-line regression has the formula

y = 11.23 - 0.4667x ± 2.0738

(r = -0.70638), which is a slightly better fit, but neither is a particularly good fit, as shown by the

rms errors and the correlation factors

Each indicates a decrease in bid with an increase in bidders.

Decision: Reject the Null (p=0.70). There is a significant positive relationship between the

number of bidders and the amount of winning bid on highway projects.

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4. Cardio Glide

Answer:Person Months owned(X) Hours exercised(Y) X* X Y*Y X*Y

Jim 12 4 144 16 48

Claire 2 10 4 100 20Juan 6 8 36 64 48

Neil 9 5 81 25 45

Jonalyn 7 5 49 25 35William 2 8 4 64 16

Joshua 8 3 64 9 24

Melvin 4 8 16 64 32

John 10 2 100 4 20

James 5 5 25 25 25

Total 65 58 523 396 313

The hypothesis to be tested is:

Ho: r = 0

H1: r < 0 (hypothesizing a significant negative correlation between the two variables - a one

tailed test)

The test statistic is,. t = r Ö[(n-2)/(1-r2 )]

= - 0.8269 * Ö[(10-2)/(1-(- 0.8269)2 )]

= - 4.1593From the t-table for 0.01 level of significance and for 10-2 = 8 degrees of freedom we get the

critical value = 2.896

Since the numerical value of the test statistic is greater than the critical value we reject the null

hypothesis with 99% confidence. Hence we conclude that there is a negative association between

the number of months since the glide was purchased and the length of time the equipment wasused last week.

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5. home sample

A sample of 12 homes sold last week is selected. Can we conclude that as the size of the home

(reported below in thousands of square feet) increases, the selling price (reported in thousands)

also increases?

Home Size Selling

(thousands Price

of square feet) ( thousands)

X Y

1.4 100

1.3 110

1.2 105

1.1 120

1.4 80

1.0 105

1.3 110

0.8 85

1.2 105

0.9 75

1.1 70

1.1 95

Total 13.8 1160

Null Hypothesis: There is no significantrelationship between the size of the homeand the selling price

Alternative Hypothesis: There is asignificant relationship between the homesize and the selling price

Level of Significance: 0.05

H 1 : p0; p>0. Reject H 1 if t >

t =0076.1

212087.

= .275

Decision: Accept the null (p=.30) There isno significant relationship between the size

of the home and the selling price.

We cannot conclude that there is a positivecorrelation between the size of the

home and the selling price.

Thus, there is no association between the

home size and the selling price of 12 homes

sold

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6.

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7. Body Esteem Problem

Answer

Null Hypothesis: There is no significant difference among participants with high, medium and

low body esteem in terms of high frequency of sexual intercourse.

Alternative: There is a significant difference among participants with high, medium and low

body esteem in terms of high frequency sexual intercourse

Level of significance: 0.05

Computation: ANOVA single factor

Summary

Groups Count Sum Average VarianceHigh Body

Esteem

12 447 37.25 3777.4773

Medium BodyEsteem

12 260 21.66667 157.8788

Low Body 12 178 14.83333 109.789

Anova’

Source of Variation

SS Df MS F P-value F crit

Betweengroups

3168.167 2 1584.083 7.366186 0.002265 3.2849

Withingroups

7096.583 33 215.048

Total 10264.75 35

Decision: (F crit 3.2,F7.3) Reject the null. Therefore, there is a significant difference among

participants who’s body esteem is high, medium and low in terms of sexual intercourse.

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8. Survey conducted at Central University

It is most appropriate to adopt a paired t-test for this problem. Hence the 2 sets of data will be

combined and tested based on their differences. There is no need to be concerned with equal or

unequal variances.

If X1 and X2 denote the weight of a student before and after, respectively, D = X2 - X1 shall

denote the difference. It is assumed that X1 and X2 are normally distributed.

Based on the data, we obtain the following results

Sample size n = 11

Sample mean D-bar = 7.364Sample standard deviation sD = 8.370

The hypotheses are

Ho: μ1 = μ2

H1: μ1 ≠ μ2

The test statistic is

T = D- bar / sD/√n = 7.364 / 8.370/√11 = 2.918

Given that α = 0.01, the critical t-value with 10 d.o.f. = 3.169

Since the test statistic does not exceed the critical t-value, we fail to reject Ho. Thus, the richer

Filipino food will cause an increase in weight.

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9. Calorie Watchers Summary of the data:

Name Weight Change

Morco GainedLim LostTan No changeYap GainedCruz LostMoran GainedChan GainedCruz LostAn LostChan Lost

There is an inverse relationship between the variables. As the months increase, the numbers of exercise decreases.

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Reject Ho. There is a negative association between months owned and hours exercised.

1. Quality control department town problem

National News SportsUndercharge 20 10Overcharge 15 30Correct Price 200 225

Total 235 265

stat.docx

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