February/March 2026 Paper 62

Last year, the time, in minutes, spent by customers in a certain shop had mean 10.5 and standard deviation 6.8. This year, the shop owner wants to test whether the mean time spent by customers has changed. He decides to choose a sample of 20 customers. A shop assistant suggests that they should choose the first 20 customers who enter the shop one morning. Give two reasons why this will not produce a random sample.

The shop owner decides to carry out the test at the 10% significance level. He chooses a random sample of 20 customers, and he finds that the mean time spent in the shop by these customers is 8.4 minutes. You should assume that these times come from a normal distribution. Which further assumption is necessary for the test?

Carry out the test.