Hello, could someone help me with these questions please.

Please solve them using the R Studio program Thanks

1) A professor would like to know whether an introductory background module in statistics will improve student performance on a diagnostic test. Students make a diagnostic test, study the module, and then make a second diagnostic test (of similar difficulty). Should the data be treated as independent or paired samples? Explain.

2) A real estate agent would like to know if the average price of a home differs between Chelmsford and Azilda. The real estate agent randomly selects 20 for-sale homes from each location to test his hypothesis. Should the data be treated as independent or paired samples? Explain.

3) Pfizer has developed a new drug for the treatment of high blood pressure. To test its efficacy, they randomly select 30 participants with high blood pressure to receive the drug, and 32 participants with high blood pressure who will not receive the drug. They record the systolic blood pressure for each participant, and the summary statistics are shown below:

Receive Drug No Drug

n1 = 30 n2=32

u1 = 137 u2=149

s1=13.2 s2=14.1

a)State the null and alternative hypotheses

b)Check the assumptions and conditions. If there is a condition/assumption that can't be checked, explain why.

c)Determine the critical value . Use .

d)Calculate the statistic. State your value for and .

Do we reject the null hypothesis? Interpret your results.

4) For the data in the previous exercise, construct a 98% confidence interval for the mean difference.

5) A city wants to know if a new advertising campaign to make citizens aware of the dangers of driving after drinking has been effective. It counts the number of drivers who have been stopped with more alcohol in their system than the law allows for each day of the week in the week before and a month after the campaign starts. The results are shown below:

Day Before After

M 5 2

Tu 4 1

W 2 1

Th 6 3

F 7 9

Sa 13 7

Su 8 7

a)State the null and alternative hypotheses

b)Calculate the mean and standard deviation of the pairwise differences

c)Calculate the standard error of the mean difference

d)Find the critical value (use an alpha of 0.025)

e)Calculate the statistic

f) Do we reject the null hypothesis? Interpret your results.

6)

The managers of a large number of stores claim that despite relatively constant sales, profits this year are greater than last year. They have achieved this by improving their supply chain and distribution operations. Read in the StoreProfits dataset and answer the following questions. Use an alpha level of 0.05 throughout.

a)Do the data support the claim that sales have been constant over the past two years? Choose and perform the appropriate test, check the assumptions, and interpret your results.

b)Do the data support the claim that profits are higher in year two compared to year one? Choose and perform the appropriate test, check the assumptions, and interpret your results.

make a grouped bar graph that shows the year one profit, year two profit, and difference between these values for each store. Give your plot an appropriate title and axis labels.

StoreProfits dataset available here: https://drive.google.com/file/d/1uUSVh_DgitRgEbqBxkfGzButvyYOS8nu/view?usp=sharing

7)

A common measure for the effect size when using the t-test is

r = r=(t2/(t2+df))

The interpretation of r is that the effect explains 100r2 %of the total variance.

For question 6b), calculate and interpret the effect size in the context of the question.