A supermarket chain believes that customers to its stores spend less than half-anhour, on average, doing their purchases. A consumer body wants to verify this claim. They observed the entry and...

A supermarket chain believes that customers to its stores spend less than half-anhour,
on average, doing their purchases. A consumer body wants to verify this claim.
They observed the entry and departure times of 100 randomly selected customers
from supermarkets in the chain. The sample average time in the store was 27.9
minutes. Assume a population standard deviation of 10.5 minutes and that shopping
time is approximately normally distributed.

a. Test the validity of the supermarket’s belief by conducting a hypothesis test
for a single mean based on the critical value. Use ? = 0.01. What conclusion
can be drawn?
b. Compute the p-value for the test in c. and draw the appropriate management
conclusion based on the p-value.