Question

QUESTION 7 A store manager wishes to compare the service times of the express checkout with the service times of the self-serve checkout. Suppose that independent random samples of 144 customers at express and 100 at self-serve checkouts were selected, and the service times for each customer was recorded. The mean and standard deviation of the sample of customers using the express checkout were 3.7 and 0.9 minutes, respectively. For the self-serve customers, the mean and standard deviation were 4.2 and 1.7 minutes, respectively (a) At the 5% level of significance is there sufficient evidence to indicate that the mean service time for customers using the express checkout is less than the mean time for customers using self- serve? Use the critical value approach, and be sure to write a concluding sentence (b) What is the p-value associated with the test in (a)? (c) Is it necessary to assume that the populations of service times for customers using express and self-serve checkouts are normally distributed? Explain your answer

Answer 1

Let u_1 and u_2 be the population means Let x_1^bar and x_2^bar be the means of the respective samples from the given information n_1 = 144, x_1^bar = 3.7, s_1 = 0.9 n_2 = 100, x_2^bar = 4.2, s_2 = 1.7 The level of significance alpha = 0.05 state the null and alternative hypothesis we are to test for the mean service time for customers using the express checkout is different from the mean service time for customer using self-serve. The null and alternative hypothesis are, respectively we need to use two-tailed test. H_0: u_1 - u_2 = 0 (There is no significant difference between the population means) \r\n H_1: mu_1 - mu_2 notequalto 0 (There is significant difference between the population means). Step 2: select the distribution to use: - Here, the two samples are independent sigma_1 and sigma_2 are unknown but equal, and the sample sizes are small but both populations are normally distributed. Hence,