4 The waiting times for patients to see a doctor in a hospital can be modelled with a normal distribution with known variance of 10 minutes.
4
- A random sample of 100 patients has a total waiting time of 3540 minutes.
Calculate a \(98 \%\) confidence interval for the population mean of waiting times, giving values to four significant figures.
4 - Dante conducts a hypothesis test with the sample from part (a) on the waiting times. Dante's hypotheses are
$$\begin{aligned}
& \mathrm { H } _ { 0 } : \mu = 38
& \mathrm { H } _ { 1 } : \mu \neq 38
\end{aligned}$$
Dante uses a \(2 \%\) level of significance.
Explain whether Dante accepts or rejects the null hypothesis.