Question: You are considering a new delivery system and wish to test whether delivery times are significantly different, on average ,than your current system. It is well established that the mean delivery time of the current system is 2.38 days. A test of the new system shows that, with 48 observations, the average delivery time is 1.91 days with a std deviation of 0.43 day.

a. Identify the null and research hypotheses for a two sided test, using both words and mathematical symbols

b. Perform a two sided test at the 5% significance level and describe the result

c. Perform a two sided test at the 1% significance level and describe the result

d. State the p-value as either p>0.05, p < 0.05, p< 0.01, or p<0.001

e. Summarize the results in a brief memo to management