A travel agency call centre wants to know the average number of calls received per day by its call centre. A random sample of 21 days is selected and the sample mean number of calls received was found to be 166.2 with a sample standard deviation of 22.8 calls. Assume that calls received daily are normally distributed.
(a) Calculate a 95% confidence interval for the mean number of daily calls received by the call centre. Interpret the findings.
(b) Find a 99% confidence interval for the mean number of daily calls received by the call centre.
(c) Compare the findings of (a) and (b) and explain the reason for the difference.
(d) Compute the confidence interval in (a) using Excel's TINV formula.
(e) Estimate, with 95% confidence, the total number of calls received over a 30-day period. Interpret the result.