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

∑ ꭓ = 205                              ∑ (ꭓ -
x̄) ² = 56.43

1. Calculate the sample mean
   x̄
   
   


2. Calculate the sample standard deviation.


3. 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.


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