| Exam Board | CAIE |
| Module | S2 (Statistics 2) |
| Year | 2022 |
| Session | March |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Two-tailed hypothesis test |
2 Harry has a five-sided spinner with sectors coloured blue, green, red, yellow and black. Harry thinks the spinner may be biased. He plans to carry out a hypothesis test with the following hypotheses.
$$\begin{aligned}
& \mathrm { H } _ { 0 } : \mathrm { P } ( \text { the spinner lands on blue } ) = \frac { 1 } { 5 }
& \mathrm { H } _ { 1 } : \mathrm { P } ( \text { the spinner lands on blue } ) \neq \frac { 1 } { 5 }
\end{aligned}$$
Harry spins the spinner 300 times. It lands on blue on 45 spins.
Use a suitable approximation to carry out Harry's test at the \(5 \%\) significance level.