A supermarket chain believes that customers to its stores spend half-an-hour or more, on average, doing their purchases. A consumer body wants to verify this claim. They observed the entry and departure times of 86 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) Formulate the null and alternative hypothesis for this test scenario.

(b) Which test statistic (z or t) is appropriate for this test? Why?

(c) Test the validity of the supermarket's belief by conducting a hypothesis test for a single mean. Use α = 0.01. What conclusion can be drawn?

(d) Use Excel's NORMSDIST function to compute the p-value for the test and draw the appropriate management conclusion based on the p-value.