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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

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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