Mathematics 9709 · AS & A Level · Hypothesis testing

Hypothesis testing — practice question

It is given that $8\%$ of adults in one town own a Chantor car. Following an advertising campaign, a car dealer wants to find out whether this proportion has gone up. He selects a random sample of $25$ adults from the town and records how many own a Chantor car.
(a)[5]

He discovers that $4$ of the $25$ adults own a Chantor car. Carry out a hypothesis test at the $5\%$ significance level.

(b)[2]

Explain which error, Type I or Type II, could have occurred when carrying out the test in part (a).

(c)[3]

Later, the car dealer selects another random sample of $25$ adults from the town and performs a similar hypothesis test at the $5\%$ significance level. Find the probability of a Type I error.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: State $H_0:p=0.08$, with $H_1:p>0.08$

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