(1) In each of the following scenarios, determine if the data are paired.

(a) Compare pre- (beginning of the semester) and post-test (end of the semester) scores for the same group of students.

(b) Assess the gender-related salary gap by comparing salaries of randomly sampled men and women.

(c) Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.

(d) Assess the effectiveness of a diet regimen by comparing the before and after weights of subjects.

(e) We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To find out, we take a random sample of 50 days and record Intel's stock, then we take another sample of 50 days and record the Southwest's stock.

(f) In order to test whether there is a significant difference in the pricing at Target and Walmart, we randomly sample 50 items from Target store and note the price for each. Then we visit Walmart and note the price for each of those same 50 items.For each item, the prices from the two stores are listed next to each other in the same row.

(g) A school board would like to determine whether there is a difference in average SAT scores for students at one high school versus another high school in the district. To check, they take a simple random sample of 100 students from each high school.

(2)A first sample of 28 men who were recovering from a heart attack and a second independently selected sample of 30 men who had not had a heart attack was taken with the goal of comparing mean cholesterol levels. The men in the samples were the same age. Researchers were investigating whether the mean cholesterol for the men who were recovering from heart attacks would be higher than the mean level for the other men.

The means and the standard deviations for the two groups are shown below.

Sample

N

Mean

StDev

Sample 1

28

253.9

47.7

Sample 2

30

193.1

22.3

₁ represents the population mean for group 1(individuals recovering from heart attacks)

₂ represents the population mean for group 2(individuals recovering from heart attacks)

a)Write the appropriate null- and alternative hypotheses,

b)Use Minitab to test the hypothesis for the difference in two means.

c)What is the t-value and the p-value?

d)What is the decision regarding the null hypothesis? Use a 5% significance level.

e) What is the conclusion regarding the investigation?

(3) Researchers collected a simple random sample of 36 children who had been identified

as gifted in a large city. The following table shows the mean and standard deviation of the IQ scores of mothers and fathers of these children.

Use the independent samples t-test to test whether the mean IQs of mothers of gifted children are significantly different from the mean IQs of fathers of gifted children.

b)Write the appropriate null- and alternative hypotheses,

b)Use Minitab to test the hypothesis for the difference in two means.

c)What is the t-value and the p-value?

d)What is the decision regarding the null hypothesis? Use a 5% significance level.

e) What is the conclusion regarding the investigation?

(4) Open the attached Excel file and copy the data into Minitab.The Freshman BMI Data includes the BMI levels of college students at the beginning of the school year in September and at the end of the school year in April. Use a paired t-test to test whether there is a significant difference between the two BMI levels.

a) Write the appropriate null- and alternative hypotheses,

b) Use Minitab to test the hypothesis for the Paired t-test for difference in the two means.

c)What is the t-value and the p-value?

d)What is the decision regarding the null hypothesis? Use a 5% significance level.

e) What is the conclusion regarding the investigation?

(5) A study determined the number of cavity-free children per 100 children in 16 North American cities before and after public water fluoridation projects. This is paired data since the before and after values come from the same cities. The mean and the standard deviation of the difference between the data before and after the fluoridation is given below.Test the hypothesis that the number of cavities is significantly lower after the fluoridation. Use 5% level for the significance

(d= the difference between the number of cavities after and before the fluoridation)

Sample size: 16

Mean (diff)= -12.31

Standard Deviation (diff)=13.92

a) Write the appropriate null- and alternative hypotheses,

b) Use Minitab to test the hypothesis for 1-sample t for the difference in the two means. (Copy the Minitab results below)

c)What is the t-value and the p-value?

d) What is the decision regarding the null hypothesis? Use a 5% significance level.

e) What is the conclusion regarding the investigation?

f) With the same mean and the standard deviation, run the 1-sample hypothesis test when the sample size is 5. (Copy the Minitab results below)

g) At a 5% level of significance, is the null hypothesis rejected?

h) How do the answers in parts d and g compare? If there is a difference in the answers for d and g, what might be the reason for that?