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R/L handed

brokendesk

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Lecturer’s desk

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1

MGMT 276: Statistical Inference in Management

Spring 2015

Before our next exam (March 24th) Lind (5 – 11)

Chapter 5: Survey of Probability ConceptsChapter 6: Discrete Probability DistributionsChapter 7: Continuous Probability DistributionsChapter 8: Sampling Methods and CLTChapter 9: Estimation and Confidence IntervalChapter 10: One sample Tests of HypothesisChapter 11: Two sample Tests of Hypothesis

Plous (10, 11, 12 & 14)Chapter 10: The Representativeness HeuristicChapter 11: The Availability HeuristicChapter 12: Probability and RiskChapter 14: The Perception of Randomness

Schedule of readings

By the end of lecture today 3/10/15

Use this as your study guide

Confidence Intervals

Logic of hypothesis testingSteps for hypothesis testing

Levels of significance (Levels of alpha)what does p < 0.05 mean?what does p < 0.01 mean?

One-tail versus Two-tail testType I versus Type II Errors

Exam 2 –Tuesday March 24th

Study guide is online

Bring 2 calculators (remember only simple calculators, we can’t use

calculators with programming functions)

Bring 2 pencils (with good erasers)Bring ID

Stats Review by Jonathon & Nick

When: Monday evening March 23rd

7:30 – 9:30pm(Immediately following Accounting review)

McClelland Hall 207(Berger Hall)

Cost: $5.00

No HomeworkJust study for

exam

Have a safe and happy

spring break

No class on Thursday

.

Review of Homework Worksheet

just in case of questions

Homework Worksheet:

Confidence interval uses SEM

z scores for differentlevels of confidence

Level of Alpha

1.96

= .05

2.58

= .01

1.64

= .10

90%

How do we know which z score to

use?

2.58sd

2.58 sd

.99? 55 ?

Homework Worksheet: Problem 1

Standard deviation = 10

Mean = 55

Upper boundary raw scorex = mean + (z)(standard deviation)x = 55 + (+ 2.58)(10)x = 80.8Lower boundary raw scorex = mean + (z)(standard deviation)x = 55 + (- 2.58)(10)x = 29.2

29.280.8

29.2

80.8

2.58sem

2.58 sem

.99? 55 ?


Standard deviation = 10

Mean = 55

Upper boundary raw scorex = mean + (z)(standard error mean)x = 55 + (+ 2.58)(1.42)x = 58.7

Lower boundary raw scorex = mean + (z)(standard error mean)x = 55 + (- 2.58)(1.42)x = 51.3

29.280.8

51.3

58.7

10

49

1.42

51.358.7


29.280.8

58.7

8.02 8.6 9.18

7.8 8.6 9.4

51.3

10.229.8

23.116.9

4.0913.11

9.188.02

2.6714.5 9.4

7.8

Confidence Interval of 99%Has and alpha of 1%

α = .01


α = . 10


α = .05

99%

95%

90%

Area outside confidence interval is

alpha

Area in the tails is called

alpha

Area associated with most

extreme scores is called alpha

Critical z-2.58

Critical z2.58

Critical z-1.96

Critical z1.96

Critical z-1.64

Critical z1.64

Rejecting the null hypothesis

The result is “statistically significant” if:• the observed statistic is larger than the critical statistic

observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x2) to be big!!

• the p value is less than 0.05 (which is our alpha)p < 0.05 If we want to reject the null, we want our “p” to be small!!

• we reject the null hypothesis

• then we have support for our alternative hypothesis

A note on decision making following procedure versus being right relative to the “TRUTH”

. Decision making:Procedures versus outcomeBest guess versus “truth”

What does it mean to be correct?

Why do we say:• “innocent until proven guilty”• “not guilty” rather than “innocent”

Is it possible we got a verdict wrong?

.

.We make decisions at Security Check Points

.

.Type I or Type II error?

Does this airline passengerhave a snow globe?

Null Hypothesis means she does not have a snow globe

(that nothing unusual is happening) – Should we reject it???!!

As detectives, do we accuse her of brandishing a snow globe?

.

Decision madeby experimenter

Status of Null Hypothesis(actually, via magic truth-line)

Reject Ho

“yes snow globe, stop!”

Do not reject Ho

“no snow globe move on”

True Ho

No snow globe

False Ho

Yes snow globe

You are right!Correct decision

You are wrong!Type I error(false alarm)


You are wrong!Type II error

(miss)

Are we correct or have we made a

Type I or Type II error?

Does this airline passenger

have a snow globe?

Note: Null Hypothesis means she does not have a snow globe (that nothing unusual is happening) – Should we reject it???!!

.

Type I or type II error?

Does this airline passenger have a snow globe?

Type I error: Rejecting a true null hypothesisSaying the she does have snow globe when in fact she does not (false alarm)

Type II error: Not rejecting a false null hypothesis

Saying she does not have snow globe when in fact she does (miss)

What would null hypothesis be?

This passenger does not have any snow globe

Two ways to be correct:• Say she does have snow globe when she does have snow globe• Say she doesn’t have any when she doesn’t have any

Two ways to be incorrect:• Say she does when she doesn’t (false alarm)• Say she does not have any when she does (miss)

Which is

worse?


Reject Ho

Do notReject Ho

True Ho False Ho





(miss)

.

Type I or type II error

Does advertising affect sales?

Type I error: Rejecting a true null hypothesisSaying the advertising would help sales, when it really wouldn’t help people (false alarm)


Saying the advertising would not help when in fact it would (miss)


This new advertising has no effect on sales

Two ways to be correct:• Say it helps when it does• Say it does not help when it doesn’t help

Two ways to be incorrect:• Say it helps when it doesn’t• Say it does not help when it does

Which is

worse?


Reject Ho

Do notReject Ho

True Ho False Ho





(miss)

.

What is worse a type I or type II error?

What if we were lookingat a new HIV drug that had no unpleasant side affects

Type I error: Rejecting a true null hypothesisSaying the drug would help people, when it really wouldn’t help people (false alarm)


Saying the drug would not help when in fact it would (miss)


This new drug has no effect on HIV

Two ways to be correct:• Say it helps when it does• Say it does not help when it doesn’t help

Two ways to be incorrect:• Say it helps when it doesn’t• Say it does not help when it does

Which is

worse?


Reject Ho

Do notReject Ho

True Ho False Ho





(miss)

.


What if we were looking to see if there is a fire burning in an apartment building full of cute puppies

Type I error: Rejecting a true null hypothesis (false alarm)

Type II error: Not rejecting a false null hypothesis (miss)


No fire is occurring

Two ways to be correct:• Say “fire” when it’s really there• Say “no fire” when there isn’t one

Two ways to be incorrect:• Say “fire” when there’s no fire (false alarm)• Say “no fire” when there is one (miss)

Which is

worse?

.


What if we were looking to see if an individualwere guilty of a crime?

Type I error: Rejecting a true null hypothesisSaying the person is guilty when they are not (false alarm)Sending an innocent person to jail (& guilty person to stays free)


Saying the person in innocent when they are guilty (miss)Allowing a guilty person to stay free


This person is innocent - there is no crime here

Two ways to be correct:• Say they are guilty when they are guilty• Say they are not guilty when they are innocent

Two ways to be incorrect:• Say they are guilty when they are not• Say they are not guilty when they are

Which is

worse?

Rejecting the null hypothesis

The result is “statistically significant” if:• the observed statistic is larger than the critical statistic

(which can be a ‘z” or “t” or “r” or “F” or x2) observed stat > critical stat

If we want to reject the null, we want our t (or z or r or F or x2) to be big!!

• the p value is less than 0.05 (which is our alpha)p < 0.05 If we want to reject the null, we want our “p” to be small!!

• we reject the null hypothesis

• then we have support for our alternative hypothesis

How would the critical z change?

α = 0.05

Significance level = .05

α = 0.01


-1.96 or

+1.96

-2.58 or

+2.58

What if our observed z = 2.0?

Reject the null

Do notReject the null

Remember,reject the null if the observed z is bigger than the critical z

Deciding whether or not to reject the null hypothesis.05 versus .01 alpha levels

p < 0.05Yes, Significant

difference

Not a Significant difference


α = 0.05


α = 0.01


-1.96 or

+1.96

-2.58 or

+2.58


Do NotReject the null

Do NotReject the null






α = 0.05


α = 0.01


-1.96 or

+1.96

-2.58 or

+2.58

What if our observed z = -3.9?

Reject the null

Reject the null




difference


difference


α = 0.05


α = 0.01


-1.96 or

+1.96

-2.58 or

+2.58

What if our observed z = -2.52?

Reject the null





difference


z score = 1.64

One versus two tail test of significance:Comparing different critical scores

(but same alpha level – e.g. alpha = 5%)

One versus two tailed test of significance

How would the critical z change?Pros and cons…

5%

95%

2.5%

95%

2.5%

One versus two tail test of significance5% versus 1% alpha levels

-1.64 or

+1.64


One-tailed Two-tailed

α = 0.05


α = 0.01


-1.96 or

+1.96

-2.33 or

+2.33

-2.58 or

+2.58

5% 2.5% 2.5%1% .5%.5%

-1.64 or

+1.64



α = 0.05


α = 0.01


-1.96 or

+1.96

-2.33 or

+2.33

-2.58 or

+2.58


Reject the null

Reject the null





-1.64 or

+1.64



α = 0.05


α = 0.01


-1.96 or

+1.96

-2.33 or

+2.33

-2.58 or

+2.58


Reject the null






-1.64 or

+1.64



α = 0.05


α = 0.01


-1.96 or

+1.96

-2.33 or

+2.33

-2.58 or

+2.58


Reject the null

Reject the null

Reject the null




Five steps to hypothesis testing

Step 1: Identify the research problem (hypothesis)

Describe the null and alternative hypotheses

Step 2: Decision rule

• Alpha level? (α = .05 or .01)?

Step 3: Calculations

Step 4: Make decision whether or not to reject null hypothesisIf observed z (or t) is bigger then critical z (or t) then reject null

Step 5: Conclusion - tie findings back in to research problem

• One or two tailed test?• Balance between Type I versus Type II error• Critical statistic (e.g. z or t or F or r) value?

What if we were looking to see if our new management program provides different results in employee happiness than the old program. What is the independent variable?

a. The employees’ happinessb. Whether the new program works betterc. The type of management program (new vs old)d. Comparing the null and alternative hypothesis

One or two tailed test?

The type of management program

(new vs old)

Two tailed because there is no prediction

regarding who which will work better

Marietta is a manager of a movie theater. She wanted to know whetherthere is a difference in concession sales for afternoon (matinee) movies vs. evening movies. She took a random sample of 25 purchases fromthe matinee movie (mean of $7.50) and 25 purchases from the evening show (mean of $10.50). She compared these two means. This is an example of a _____.a. correlationb. t-test c. one-way ANOVAd. two-way ANOVA

What type of analysis is this?

Let’s try oneThis is an example of a

a. between participant designb. within participant designc. mixed participant design

Let’s try another one

t-test

Between

What if we were looking to see if our new management program provides different results in employee happiness than the old program. What is the dependent variable?

a. The employees’ happinessb. Whether the new program works betterc. The type of management program (new vs old)d. Comparing the null and alternative hypothesis

happiness

a. None of the employees are happyb. The program does not affect employee happinessc. The new programs works betterd. The old program works better

What if we were looking to see if our new management program provides different results in employee happiness than the old program. What would null hypothesis be?

Remember the null says “no difference between groups”

(between levels of IV)

No difference

Which of the following is a Type I error:a. We conclude that the program works better when it fact it doesn’tb. We conclude that the program works better when in fact it doesc. We conclude that the program doesn’t work better when in fact it doesn’td. We conclude that the program doesn’t work better when in fact it does

False alarm

Which of the following would represent a one-tailed test?a. Please test to see whether men or women are tallerb. With an alpha of .05 test whether advertising increases salesc. With an alpha of .01 test whether management strategies

affect worker productivityd. Does a stock trader’s education affect the amount of money they make in a year?

Increases

Which of the following represents a significant finding:a. p < 0.05b. critical value exceeds the observed statisticc. the observed z statistic is nearly zerod. we reject the null hypothesise. Both a and d Careful with

“exceeds”

p < 0.05 and “reject null” both mean

“significant finding”

Let’s try one

Marietta took a pregnancy test. The null hypothesis would be: a. Marietta is pregnant b. Marietta is not pregnant“nothing going

on”

Let’s try one

Marietta took a pregnancy test and it read that she was pregnant, when it fact she was not. This is an example of a a. Type I error b. Type II error c. Type III error d. Correct decision

False alarm = Type I error

Let’s try one

Kenley decided to reject the null, and then found out the null was false. This is an example of a a. Type I error b. Type II error c. Type III error d. Correct decision

It is right to reject a false null

Let’s try one

Agnes compared the heights of the women’s gymnastics team and the women’s basketball team. If she doubled the number of players measured (but ended up with the same means) what effect would that have on the results?

a. as the sample size got larger the variability would increase b. as the sample size got larger the variability would decreasec. as the sample size got larger the variability would stay the same

As n goes up,

variability goes down

As n ↑

According to the Central Limit Theorem, which is false?

As n ↑ x will approach µ

As n ↑ curve will approach normal shape

As n ↑ curve variability gets larger

a.

b.

c.

d. As n goes

up, variability goes down

Let’s try one

Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. Which of the following is true?

a. The IV is gender while the DV is time to finish a raceb. The IV is time to finish a race while the DV is gender

IV = genderDV = time

Let’s try one

a. The null hypothesis is that there is no difference in race times between the gendersb. The null hypothesis is that there is a difference between the genders


No difference

Let’s try one

Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. A Type I Error would claim that:

a. There is a difference when in fact there isb. There is a difference when in fact there isn’t onec. There is no difference when in fact there isn’t oned. There is no difference when in fact there is a difference

Which would be a Type II

error?

Type I =False Alarm

Type II =Miss

Let’s try one

Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides.. He concluded p < 0.05 what does this mean?

a. There is a significant difference between the meansb. There is no significant difference between the means

p < 0.05 and “reject null” both mean

“significant finding”

Let’s try one

Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. Which is true?

a. This is a one-tailed testb. This is a two-tailed test

There is no prediction regarding who will be

faster, males or females

Let’s try one


a. This is a quasi, between participant designb. This is a quasi, within participant designc. This is a true, between participant designd. This is a true, within participant design

quasi, between

Let’s try one

Albert compared the time required to finish the race for 20 female jockeys and 20 male jockeys riding race horses. He wanted to know who averaged faster rides. Which of the following is best describes this study?

a. correlationb. t-testc. one-way ANOVAd. two-way ANOVA

“t for two”(two groups being compared)

-1.64 or

+1.64

Critical z values


α = 0.05


α = 0.01


-1.96 or

+1.96

-2.33 or

+2.33

-2.58 or

+2.58

5% 2.5% 2.5%1% .5%.5%

Match each level of significance to each situation. Which situationwould be associated with a critical z of 1.96?a. Ab. Bc. Cd. D

A B

C D

Hint:Possible values

1.641.962.332.58

-1.64 or

+1.64

Critical z values


α = 0.05


α = 0.01


-1.96 or

+1.96

-2.33 or

+2.33

-2.58 or

+2.58

5% 2.5% 2.5%1% .5%.5%


A B

C D


1.641.962.332.58

An advertising firm wanted to know whether the size of an ad in the margin of a website affected sales. They compared 4 ad sizes (tiny, small, medium and large). They posted the ads and measured sales. This is an example of a _____.

a. correlationb. t-testc. one-way ANOVAd. two-way ANOVA

Relationship between advertising space and sales

More than two groups being

compared

Afra was interested in whether caffeine affects time to complete a cross-word puzzle, and whether this affected young adults and older adults similarly. This is an example of

a. correlationb. t-testc. one-way ANOVAd. two-way ANOVA.

Let’s try one

Two separate IVs1. caffeine – two levels

(yes caffeine vs no caffeine)

2. Age – two levels(young vs old)

http://www.simpsonschannel.com/screenshots/kabf19.jpg

Gabriella is a manager of a movie theater. She wanted to know whetherthere is a difference in concession sales between teenage couples andmiddle-aged couples. She also wanted to know whether time of day makes a difference (matinee versus evening shows). She gatheredthe data for a sample of 25 purchases from each pairing. a. correlationb. t-testc. one-way ANOVAd. two-way ANOVA

Relationship between movie times andamount of concession purchases.

Let’s try one

Two separate IVs1. Time of day – two levels

(afternoon vs evening)2. Age – two levels

(young vs old)

Victoria was also interested in the effect of vacation time on productivity of the workers in her department. In her department some workers took vacations and some did not. She measured the productivity of those workers who did not take vacations and the productivity of those workers who did (after they returned from their vacations). This is an example of a _____. a. quasi-experimentb. true experimentc. correlational study

Let’s try one

Quasi- experimentShe did not randomly

assign groups, she let the workers self-select who will

go on vacation

Ian was interested in the effect of incentives for girl scouts on the number of cookies sold. He randomly assigned girl scouts into one of three groups. The three groups were given one of three incentives and he looked to see who sold more cookies. The 3 incentives were: 1) Trip to Hawaii, 2) NewBike or 3) Nothing. This is an example of a ___.a. quasi-experimentb. true experimentc. correlational study

Let’s try one

True- experimentHe randomly assigned girls to

groups

Marietta is a manager of a movie theater. She wanted to know whetherthere is a difference in concession sales for afternoon (matinee) movies vs. evening movies. She took a random sample of 25 purchases fromthe matinee movie (mean of $7.50) and 25 purchases from the evening show (mean of $10.50). She compared these two means. This is an example of a _____.a. correlationb. t-test c. one-way ANOVAd. two-way ANOVA


Let’s try one


Marietta is a manager of a movie theater. She wanted to know whetherthere is a difference in concession sales for afternoon (matinee) movies and evening movies. She took a random sample of 25 purchases fromthe matinee movie (mean of $7.50) and 25 purchases from the evening show (mean of $10.50). Which of the following would be the appropriate graph for these data


Let’s try one

Matinee Evening

Conce

ssio

npurc

hasea.

Movie Time

Conce

ssio

n

b.

Movie Times

Conce

ssio

npurc

hased.

c.

Conce

ssio

npurc

hase

Movie Times


Pharmaceutical firm tested whether fish-oil capsules taken daily decrease cholesterol. They measured cholesterol levels for 30 male subjects and then had them take the fish-oil daily for 2 months andtested their cholesterol levels again. Then they compared the meancholesterol before and after taking the capsules. This is an example of a _____.a. correlationb. t-testc. one-way ANOVAd. two-way ANOVA

Relationship between daily fish-oil capsules and cholesterol levels in men.

Let’s try oneThis is an example of a

a. between participant designb. within participant designc. mixed participant design

Let’s try another one

“t for two”(fish-oil vs no fish-oil are the two groups being compared)

Within (same people measured

twice)

Elaina was interested in the relationship between the grade pointaverage and starting salary. She recorded for GPA. and startingsalary for 100 students and looked to see if there was a relationship. This is an example of a _____.a. correlationb. t-testc. one-way ANOVAd. two-way ANOVA

Relationship between GPA and starting salary

Let’s try one

Relationship between GPA and Starting salary

GPA

Sta

rtin

g

Sala

ry

Correlation(both variables are

quantitative)

An automotive firm tested whether driving styles can affect gas efficiencyin their cars. They observed 100 drivers and found there were four general driving styles. They recruited a sample of 100 drivers all of whom drove with one of these 4 driving styles. Then they asked all 100 drivers to use the same model car for a month and recorded their gas mileage. Then they compared the mean mpg for each driving style.This is an example of a _____.a. correlationb. t-testc. one-way ANOVAd. two-way ANOVA

Relationship between driving strategy and gas mileage (miles per gallon).

ANOVAFour groups being

compared

Afra was interested in which characteristics of displays around the cash register will affect impulse purchases of candy bars and drinks. She was interested in the type of display (big versus little) and the location of the display (eye level versus waist level). She varied the location and type of display on different registers and recorded the number of sales of items on the displays (candy and drinks). This is an example ofa. correlationb. t-testc. one-way ANOVAd. two-way ANOVA.

Let’s try one

Two separate IVs1. Type of display – two

levels (big vs little)

2. Location – two levels(eye vs waist level)

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