5 Last year the mean time for pizza deliveries from Pete's Pizza Pit was 32.4 minutes. This year the time, \(t\) minutes, for pizza deliveries from Pete's Pizza Pit was recorded for a random sample of 50 deliveries. The results were as follows.
$$n = 50 \quad \Sigma t = 1700 \quad \Sigma t ^ { 2 } = 59050$$
- Find unbiased estimates of the population mean and variance.
- Test, at the \(2 \%\) significance level, whether the mean delivery time has changed since last year.
- Under what circumstances would it not be necessary to use the Central Limit Theorem in answering (b)?