(10 points) A random sample of workers is selected in a city. Their commute time an minutes) from home to work and from work to home are recorded and shown below. Woker 1 2 3 4 5 6 7 From home to work 25 24 26 25 24 27 25 From work to home 44 40 37 27 23 25 39 Suppose that we want to test whether the mean commute time from home to work and from work to home is different for all workers in this city. Part A State the null and alternative hypotheses. Let [M be the mean difference in the commute time between from work to home and from home to work for all workers. Note: The difference in the commute time is defined as [From home to work] [From work to home]. Part B The test statistic for the hypothesis test is . (Round the test statistic to 5 decimal places) Part C At the 5% significance level, what can you conclude? Since the the absolute value of test statistic is ? v than the critical value, , the p-value is ? v than 0.05. At the 5% significance level, we 7 v . Therefore, the sample data provide ? v evidence to support that the mean commute time from home to work and from work to home is different for all workers in this city. . Part D Use an appropriate 90% confidence interval to complete the following. (Round the confidence interval to 5 decimal places) In the population of all workers in this city, the mean commute time from home to work is 7 v from work to home by between and minutes