| Exam Board | AQA |
|---|
| Module | Further Paper 3 Statistics (Further Paper 3 Statistics) |
|---|
| Year | 2019 |
|---|
| Session | June |
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| Topic | Hypothesis test of a normal distribution |
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2 Amy takes a sample of size 50 from a normal distribution with mean \(\mu\) and variance 16
She conducts a hypothesis test with hypotheses:
$$\begin{aligned}
& \mathrm { H } _ { 0 } : \mu = 52
& \mathrm { H } _ { 1 } : \mu > 52
\end{aligned}$$
She rejects the null hypothesis if her sample has a mean greater than 53
The actual population mean is 53.5
Find the probability that Amy makes a Type II error.
Circle your answer.
\(0.4 \% 3.9 \% 18.9 \% 15.0 \%\)