Waiting_Time DataSet:

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1

A manager of a large grocery store wants to increase the customer service satisfaction rate. He is thinking about giving a 5% discount to customers who wait in line more than 8 minutes. However, to get a better idea about the current waiting times, she hired a student to measure the time spent by customers waiting in line. Using a stopwatch, the student determined the amount of time between the time a customer joined the line and the time he or she reached the teller. The times for a random sample of 50 customers were recorded in the dataset waiting time. a) Examine a boxplot and a histogram of the Time variable. Display these two plots and explain if you would expect the means of all possible random waiting time samples of size 50 from the costumer population to follow a normal distribution. b) Compute the sample mean and the standard error of the mean. Answer the following questions regardless of your answer to part a). In other words, assume that all the required conditions are satisfied. c) The store manager would like to determine whether there is enough evidence suggesting that the mean waiting time for the grocery store's customers is less than 6 minutes. Conduct the corresponding hypothesis test using a 10% significance level and the p-value approach. d) Construct the appropriate one-sided 90% confidence interval for the true mean waiting time for the grocery store's customers. Is this interval consistent with your conclusion in parts c) above? Explain. e) How large a sample should it be to estimate the mean waiting time for the grocery store's customers with a margin of error of 0.34 and a 90% confidence? Assume that the waiting time standard deviation is 2.86 minutes. A manager of a large grocery store wants to increase the customer service satisfaction rate. He is thinking about giving a 5% discount to customers who wait in line more than 8 minutes. However, to get a better idea about the current waiting times, she hired a student to measure the time spent by customers waiting in line. Using a stopwatch, the student determined the amount of time between the time a customer joined the line and the time he or she reached the teller. The times for a random sample of 50 customers were recorded in the dataset waiting time. a) Examine a boxplot and a histogram of the Time variable. Display these two plots and explain if you would expect the means of all possible random waiting time samples of size 50 from the costumer population to follow a normal distribution. b) Compute the sample mean and the standard error of the mean. Answer the following questions regardless of your answer to part a). In other words, assume that all the required conditions are satisfied. c) The store manager would like to determine whether there is enough evidence suggesting that the mean waiting time for the grocery store's customers is less than 6 minutes. Conduct the corresponding hypothesis test using a 10% significance level and the p-value approach. d) Construct the appropriate one-sided 90% confidence interval for the true mean waiting time for the grocery store's customers. Is this interval consistent with your conclusion in parts c) above? Explain. e) How large a sample should it be to estimate the mean waiting time for the grocery store's customers with a margin of error of 0.34 and a 90% confidence? Assume that the waiting time standard deviation is 2.86 minutes