Part II. Questions. Try to answer questions in the space provided under each question and show all calculations. Please clearly indicate your final answer for each sub-question. 23. A university has taken a random sample of 16 students. The average length of time it took the students in the sample to take a placement test was 65 minutes. The population standard deviation is known to be 8 minutes. We want to determine whether the mean test time of all students is significantly less than 70 minutes. a. State the null and alternative hypotheses. (3 points) b. Calculate the p-value. (4 points) c. Use the p-value approach to test the hypothesis at the 5% level of significance. (5 points)

24. Given below are ten observations collected in a regression study on independent variable x and dependent variable y. Use Excels Regression Tool to answer the following question and attach your Excel file. x y 5.90 1.27 5.82 1.32 5.15 1.22 5.83 1.31 4.81 1.28 5.22 1.19 4.68 1.16 5.18 1.14 4.80 1.14 5.04 1.17 a. Show the scatterplot. (4 points) b. What is the coefficient of determination in this regression? What is the test statistic for variable x? (4 points) c. What are the decision and conclusion on testing whether there is any linear relationship between x and y at 1% level of significance? (3 points)