David 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. David 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. David surveys a random sample of 17 workers who have the Unlimited plan and a random sample of 15 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 11, 17, 30, 26, 25, 18, 19, 10, 18, 19, 11, 15, 24, 18, 9, 19, 18 Traditional Send data to calculator 21, 16, 17, 15, 16, 15, 15, 14, 18, 15, 16, 13, 18, 17, 11 Send data to Excel Assume that the two populations of vacation days taken are approximately normally distributed. Can David conclude, at the 0.05 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 Ho and the alternate hypothesis H. Ho H :] : (b) Determine the type of test statistic to use. S P t Degrees of freedom: = (c) Find the value of the test statistic. (Round to three or more decimal places.) O X (d) Find the n-value (Dound to thron or more decimal places