A company wants to check the quality of its customer service regarding phone enquiries. For this reason, the manager wants to compare the call waiting times during the years 2020 and 2019. Unfortunately, extensive records of the company are not available, and he can only check a random sample of phone calls within these two years. The available data, measured in minutes of waiting time, are provided below for each year.

Sample size Sample mean Sample standard deviation

2020 42 7.4 0.5

2019 35 7.1 0.6

(a) Use an appropriate hypothesis test to determine whether the mean waiting times were different between these two years. Test at two appropriate signifi cance levels, stating clearly the hypotheses, the test statistic and its distribution under the null hypothesis. Comment on your findings.

(b) State clearly any assumptions you made in (a).

(c) Adjust the procedure above to determine whether the mean waiting time in 2020 was greater than in 2019.