- A machine makes posts. The length of a post is normally distributed with unknown mean \(\mu\) and standard deviation 4 cm .
A random sample of size \(n\) is taken to test, at the \(5 \%\) significance level, the hypotheses
$$\mathrm { H } _ { 0 } : \mu = 150 \quad \mathrm { H } _ { 1 } : \mu > 150$$
- State the probability of a Type I error for this test.
The manufacturer requires the probability of a Type II error to be less than 0.1 when the actual value of \(\mu\) is 152
- Calculate the minimum value of \(n\).