Ryan is a human resources executive for a technology company

Last updated: 5/27/2023

Ryan 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 Ryan 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 Ryan 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 For the workers with an Unlimited plan the sample mean is 18 2 with a sample variance of 24 7 For the workers with a Traditional plan the sample mean is 14 9 with a sample variance of 5 4 Assume that the two populations of vacation days taken are approximately normally distributed Can Ryan 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 H 0 0 H 0 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 05 level of significance can Ryan 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 Yo No H X 9 O S 0 0 OSO X P G B alo 0 0 0 0 20