A mail-order business prides itself in its ability to fill customers' orders in six calendar days or less on the average. Periodically, the operations manager chooses a random sample of customer orders and finds out the number of days needed to fill their orders. Based on this sample information, he decides whether the desired standard is being met. He will suppose that the average number of days to fill customer orders is six or less unless the data strongly suggest otherwise.
a. Establish the appropriate null as well as alternative hypotheses.
b. On one occasion where a sample of 40 customers was selected, the average number of days was 6.65, with the sample standard deviation of 1.5 days. Can the operations manager conclude that this mail-order business is achieving its goals?
Explain. Employ a significance level of 0.025 to answer this question.