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Lesson 9: Comparing Two Groups

 

 

NAME

 

 

Lab Activity

 

 

Answer the following questions showing all work. For questions

 

that require Minitab Express include the appropriate output (copy

 

+ paste) along with an explanation. For all tests use an alpha level

 

of .05 unless otherwise specified.

 

1. For each of the following scenarios, which of the following hypothesis

 

tests is most appropriate: one sample proportion, one sample mean,

 

two independent proportions, two independent means, or two paired

 

(dependent) means? Explain why. (30 points)

 

a) single mean test which is one tailed[z test]

 

b) two proportion test which is one tailed[z test]

 

c) two proportion test which is one tailed[z test]

 

d) two proportion test which is one tailed[z test]

 

e) Single proportion test which is two tailed[z test]

 

f) two proportion test which is one tailed[z test]

 

g) Two mean test which is two tailed

 

 

A. A bakery advertises that their cupcakes weigh 100 grams. A group of

 

customers believe that this is false advertising and that the average

 

weight of this bakery?s cupcakes is really less than 100 grams.

 

 

B. The physics department at one college wants to know if physics

 

majors? SAT-Math scores are higher than their SAT-Verbal scores. They

 

take a simple random sample of 30 physics majors and ask each student

 

for his or her SAT-Math and SAT-Verbal scores.

 

 

C. The admissions office at a liberal arts school wants to know if

 

applicants to their music education program have higher SAT-Verbal

 

scores than applicants to their elementary education program.

 

 

D. Students at Penn State and Michigan State are arguing over which

 

university?s students have better SAT-Writing essay scores. They take a

 

 

Lesson 9: Comparing Two Groups

 

 

NAME

 

 

Lab Activity

 

 

random sample of 50 students from each university and record their

 

SAT-Writing essay scores.

 

 

E. In the population of all Penn State World Campus students, 18.6%

 

have military experience. An instructor at Penn State Harrisburg wants

 

to know if the proportion of students at Penn State Harrisburg is

 

different from 18.6%. She takes a random sample of 100 Penn State

 

Harrisburg students and asks if they?ve had military experience.

 

 

F. A group of developmental psychologists are conducting a study on

 

male/female fraternal twins. They want to know if the female twins

 

tend to have higher emotional intelligence scores than their male twin

 

counterparts. They have a sample of 20 male/female fraternal twins

 

and give each an emotional intelligence test.

 

 

G. Nursing students want to compare the resting heart rates of college

 

students who exercise regularly and college students who do not

 

exercise regularly. They have a sample of 100 college students: 60 who

 

claim to exercise regularly and 40 do not. They measure each

 

individual?s resting heart rate.

 

 

H. The Department of Statistics wants to compare the proportion of men

 

and women who pass STAT200. They take a random sample of 500

 

students enrolled in STAT200 and at the end of the semester record

 

their gender and whether or not they passed the course.

 

 

I. A pharmaceutical company wants to compare the LDL cholesterol

 

levels of patients who have taken two different drugs (Drug A and Drug

 

B). They randomly assign 30 patients to receive Drug A and 30 patients

 

to receive Drug B. After taking 90 days they measure each patient?s LDL

 

cholesterol level.

 

 

Lesson 9: Comparing Two Groups

 

 

NAME

 

 

Lab Activity

 

 

J. A group of psychology students what to know if wives tend to have

 

higher marital satisfaction levels than their husbands. They have a

 

sample of 30 married heterosexual couples. The husband and wife each

 

complete a test of marital satisfaction.

 

 

Lesson 9: Comparing Two Groups

 

 

NAME

 

 

Lab Activity

 

 

2. I want to compare my students? scores on the Midterm I Practice Quiz and

 

the Midterm I exam. In a sample of 33 students, the mean difference was

 

6.159 points with a standard deviation of 15.156. Scored tended to be higher

 

on the practice quiz. Use Minitab / Minitab Express to answer the following

 

questions. You will have to enter in these statistics as ?summarized data.? (16

 

points)

 

A. Construct a 95% confidence interval for the mean difference between

 

the Midterm I Practice Quiz and Midterm I exam.

 

The obtained output is given below,

 

One-Sample T

 

Test of ? = 0 vs ? 0

 

N

 

33

 

 

Mean

 

6.16

 

 

StDev

 

15.16

 

 

SE Mean

 

2.64

 

 

95% CI

 

(0.78, 11.53)

 

 

T

 

2.33

 

 

P

 

0.026

 

 

From the above output we can see that the 95% confidence interval for the mean

 

difference between the Midterm I Practice Quiz and Midterm I exam is (0.78,

 

11.53).

 

B. Given the null hypothesis ?d = 0, and alternative hypothesis ?d? 0,

 

what is the p value?

 

From the output we can see that the required p-value is 0.026.

 

C. Is there evidence that students scored differently on the Midterm I

 

Practice Quiz and Midterm I? Why?

 

As the p-value is smaller than the significance level of 0.05 so we are rejecting the

 

null hypothesis and concluding that there is sufficient evidence that students

 

scored differently on the Midterm I Practice Quiz and Midterm I.

 

 

Lesson 9: Comparing Two Groups

 

 

NAME

 

 

Lab Activity

 

 

3. Open the SP16STUDENTDATA.MTW dataset. Assume that this is a sample

 

that is representative of the population of all World Campus STAT200 students.

 

We want to know if males and females differ in terms of what they believe is

 

the ideal age to get married. (22 points)

 

A. Write the null and alternative hypothesis using the appropriate

 

symbols.

 

 

B. Does this scenario require an independent samples or paired

 

samples t test? Why?

 

 

C. For the variable of ?ideal marriage age,? are the standard deviations

 

for males and females similar or different? (If one is more than twice of

 

the other they are different)

 

 

D. Compute the appropriate test statistic. (I strongly encourage you do

 

to this in Minitab/Minitab Express and NOT by hand)

 

 

E. What is the p value?

 

 

F. Is your decision to reject or fail to reject the null hypothesis from part

 

(A)? Why?

 

 

G. Is there statistical evidence that the ideal marriage age of males and

 

females is different on average?

 

 

H. How could you answer this research question using a confidence

 

interval? (You don?t have to actually do it, just explain what you could

 

do.)

 

 

Lesson 9: Comparing Two Groups

 

 

NAME

 

 

Lab Activity

 

 

4. Open the dataset SP16STUDENTDATA.MTW. Assume that this is a sample

 

that is representative of the population of all World Campus STAT200 students.

 

(32 points)

 

A. Construct a 95% confidence interval for the difference in the heights

 

of male and female students.

 

 

B. Interpret the 95% confidence interval that you constructed in part

 

(A).

 

 

C. Given your results from part (A), is there evidence that male and

 

female students differ in terms of their heights? Explain why?

 

 

D. Construct a 95% confidence interval for the difference in the

 

proportion of males and females who are dieting.

 

 

E. Interpret the 95% confidence interval that you constructed in part

 

(D).

 

 

F. Use the five-step hypothesis testing procedure to determine if there is

 

a difference in the proportion of Pennsylvania and non-Pennsylvania

 

residents who own a dog.

 

Step 1:

 

Step 2:

 

Step 3:

 

Step 4:

 

Step 5:

 

 



 

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