The manager at the Hillsberg Savings and Loan is interested in determining whether there is a difference in the mean time that customers spend completing their transactions depending on which of four tellers they use. To conduct the test, the manager has selected simple random samples of 15 customers for each of the tellers and has timed them (in seconds) from the moment they start their transaction to the time the transaction is completed and they leave the teller station. The manager then asked one of her assistants to perform the appropriate statistical test. The assistant returned with the following partially completed ANOVA table.

Summary Groups Count Sum Average Variance Teller 1 15 3,043.9 827.4 Teller 2 15 3,615.5 472.2 Teller 3 15 3,427.7 445.6 Teller 4 15 4,072.4 619.4 ANOVA Source of Variation SS df MS F-ratio p-value F-crit Between Groups 36,530.6 4.03E–09 2.7694 Within Groups Total 69,633.7 59

a. State the appropriate null and alternative hypotheses.

b. Test to determine whether the population variances are equal. Use a significance level equal to 0.05.

c. Fill in the missing parts of the ANOVA table and perform the statistical hypothesis test using a  0.05.

d. Based on the result of the test in part

c, if warranted, use the Tukey-Kramer method with a  0.05 to determine which teller require the most time on average to complete a customer’s transaction.