Mathematics 9709 · AS & A Level · Hypothesis testing

Hypothesis testing — practice question

Harry has a spinner with five sectors, coloured blue, green, red, yellow and black. Harry suspects that the spinner could be biased. He intends to carry out a hypothesis test with the following hypotheses: $H_0:\;P(\text{the spinner lands on blue}) = \frac{1}{5}$ and $H_1:\;P(\text{the spinner lands on blue}) \neq \frac{1}{5}$. Harry spins the spinner 300 times, and blue comes up on 45 of the spins.
(main)[5]

Apply a suitable approximation to carry out Harry’s test at the $5\%$ significance level.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Approximate $B(300,\tfrac{1}{5})$ by $N(60,48)$

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