CAIE S2 2022 March — Question 2

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2022
SessionMarch
TopicApproximating Binomial to Normal Distribution
TypeTwo-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.