4 The distance a particular football player runs in a match is modelled by a normal distribution with standard deviation 0.3 kilometres.
A random sample of \(n\) matches is taken.
The distance the player runs in this sample of matches has mean 10.8 kilometres.
The sample is used to construct a \(93 \%\) confidence interval for the mean, of width 0.0543 kilometres, correct to four decimal places.
4
- Find the value of \(n\)
4
- Find the \(93 \%\) confidence interval for the mean, giving the limits to three decimal places.
4 - Alison claims that the population mean distance the player runs is 10.7 kilometres.
She carries out a hypothesis test at the 7\% level of significance using the random sample and the hypotheses
$$\begin{aligned}
& \mathrm { H } _ { 0 } : \mu = 10.7 \\
& \mathrm { H } _ { 1 } : \mu \neq 10.7
\end{aligned}$$
4
- State, with a reason, whether the null hypothesis will be accepted or rejected.
4
- (ii) Describe, in the context of the hypothesis test in part (c)(i), what is meant by a Type II error.
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