Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
It is stated that $28\%$ of the voters in a particular town back the Forward Now political party. A researcher thinks the actual proportion is below $28\%$. She takes a random sample of $30$ voters from the town and discovers that $4$ people in the sample said they support the Forward Now party. She intends to perform a hypothesis test at the $10\%$ significance level.
(a)[5]
Carry out the test by using a binomial distribution.
(b)[1]
State, with a reason, whether a Type I error might have been made when carrying out the test.
(c)[2]
At a later stage, the researcher performs a similar test at the $10\%$ significance level, using another random sample of $30$ voters from the town. Find the probability of a Type I error.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate hypotheses $H_0:p=0.28$, $H_1:p<0.28$” …