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...

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 longdistance calls has changed. Fifty calls, originating from the town, was randomly selected and the following summary minutes.

∑ ? = 205

∑(? − ?̅)^2 = 56.43

a) Calculate the sample mean, ?̅.

b) Calculate the sample standard deviation.

c) 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.

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