Mathematics 9709 · AS & A Level · Hypothesis testing

Hypothesis testing — practice question

A spinner is split into five sectors, and each sector carries a different colour. Susma and Sanjay both want to check whether the spinner is biased so that it lands on red less often than it would if it were fair. Susma spins the spinner $40$ times, and it lands on red exactly $4$ times.
(a)[5]

Apply a binomial distribution to complete the test at the $5\%$ significance level.

(b)[3]

Sanjay spins the spinner $40$ times too, and it lands on red $r$ times. Use a binomial distribution to determine the largest $r$ that is in the rejection region for the test at the $5\%$ significance level.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct hypotheses $H_0: p = 0.2$, $H_1: p < 0.2$

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