7 In the past the weekly profit at a store had mean \(
) 34600\( and standard deviation \)\\( 4500\). Following a change of ownership, the mean weekly profit for 90 randomly chosen weeks was \(
) 35400$.
- Stating a necessary assumption, test at the \(5 \%\) significance level whether the mean weekly profit has increased.
- State, with a reason, whether it was necessary to use the Central Limit theorem in part (i).
The mean weekly profit for another random sample of 90 weeks is found and the same test is carried out at the 5\% significance level.
- State the probability of a Type I error.
- Given that the population mean weekly profit is now \(
) 36500$, calculate the probability of a Type II error.