In 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes. A telephone company wants to perform a test to determine whether this average duration of long-...

In 2015, the average duration of long-distance telephone calls from a certain town was 3.9 minutes. A telephone company wants to perform a test to determine whether this average duration of long- distance calls has changed. Fifty calls, originating from the town, was randomly selected and the following summary minutes.

∑ ? = 205                       ∑(? − ?̅)²  = 56.43

a). Using the p value approach at the 1% level of significance, test whether the mean duration of long-distance calls from the town had increased.

b). Construct the 99% confidence interval for the population mean duration of the long-distance calls from the town.