Hypothesis test for the difference ES Michael is a human resources executive for a technology company. He is deciding between two types of plans for vacation allowance for the employees of the company: Unlimited and Traditional. Michael wants to determine, for workers in the tech industry, if the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan. Michael surveys a random sample of 17 workers who have the Unlimited plan and a random sample of 16 workers who have the Traditional plan. (These samples are chosen independently.) For each worker, he records the number of vacation days taken last year. These data are shown in the table. Vacation days taken Unlimited 25, 17, 8, 7, 23, 8, 16, 17, 9, 24, 20, 8, 16, 10, 11, 18, 11 Traditional 10, 9, 10, 12, 8, 9, 9, 13, 9, 9, 11, 11, 11, 8, 7, 12 Send data to calc... v Send data to Excel Assume that the two populations of vacation days taken are approximately normally distributed. Can Michael conclude, at the 0.01 level of significance, that the population mean of the yearly number of vacation days taken by workers with an Unlimited plan is greater than the population mean of the yearly number of vacation days taken by workers with a Traditional plan? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis // and the alternate hypothesis / HO : D (b) Determine the type of test statistic to use. Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) d) Find the p-value. (Round to three or more decimal places. ) 0 e) At the 0.01 level of significance, can Michael conclude that the yearly mean number of vacation days taken by workers with an Unlimited plan is greater than the yearly mean number of vacation days taken by workers with a Traditional plan? Yes No