Mathematics 9709 · AS & A Level · Hypothesis testing

Hypothesis testing — practice question

Anton thinks that $10\%$ of students at his college are left-handed. Aliya thinks this is an underestimate. She intends to carry out a hypothesis test of the null hypothesis $p = 0.1$ against the alternative hypothesis $p > 0.1$, where $p$ is the true proportion of students at the college who are left-handed. She takes a random sample of $20$ students from the college. She will reject the null hypothesis if at least $5$ of these students are left-handed.
(a)[1]

State the meaning of a Type I error in this context.

(b)[3]

Find the probability associated with a Type I error in the test.

(c)[2]

Given that the true value of $p$ is $0.3$, find the probability that a Type II error occurs in the test.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correctly conclude that more than $10\%$ of students are left-handed (one-tailed context)

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