Lesson 9: Comparing Two Groups | Complete Solution

Answer the following questions showing all work. If you use Minitab/Minitab Express include the appropriate output (copy + paste) along with an explanation.  Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board.

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.
A. 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.   

B. 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. Assume that no student applied for both programs at the same time.

 C. 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.  

D. Students at Penn State and Michigan State are arguing over which university’s students have better SAT-Writing essay scores.  They take a 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. 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.  

H. 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.

I. 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.

2.  In Spring 2016 I wanted to compare my STAT 200 students’ scores on the Midterm Practice Quiz and the Midterm 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 Express to answer the following questions. You will have to enter in these statistics as “summarized data.”
(Hint: what are being compared in this scenario, two independent means, paired means or anything else?)
A. Construct a 95% confidence interval for the mean difference between the Midterm Practice Quiz and Midterm Exam.

B. Given the null hypothesis μd = 0, and alternative hypothesis μd≠ 0, what is the p value?

C. Is there evidence that students scored differently on the Midterm Practice Quiz and Midterm Exam? Why?

3. Open the SUMMER16STDATA.MTW dataset. Assume that this is a sample that is representative of the population of all World Campus STAT 200 students.  We want to know if males and females differ in terms of their heights.
A. Write the null and alternative hypothesis using the appropriate symbols.

B. What statistical procedure should be used to determine if there is a difference between the mean heights of males and females in the population of all World Campus STAT 200 students? Explain why

C. For the height variable, 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? Explain why

G. Is there statistical evidence that the mean heights of males and females are different in this population?

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.

I. Construct a 95% confidence interval for the difference in the proportion of males and females who are dieting.

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

K.  A research team hypothesizes that people who are dieting are more likely to eat breakfast. Use the five-step hypothesis testing procedure to determine if there is evidence to support this claim.
Step 1:
Step 2:
Step 3:
Step 4:
Step 5: