Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
A cell-phone manufacturer says that $25\%$ of students own a Pumpkin phone. Jeyeraj believes that the proportion of students at his large college who own a Pumpkin phone is below $25\%$. He intends to test the claim made by the manufacturer. He picks a random sample of $30$ students at his college. If fewer than $5$ students own a Pumpkin phone, Jeyeraj will reject the manufacturer’s claim.
(a)[1]
State appropriate hypotheses for this test.
(b)[3]
Assuming that the true proportion of students at the college who own a Pumpkin phone is $10\%$, use a binomial distribution to determine the probability of a Type II error.
(c)[3]
At Florence’s college, a random sample of $40$ students showed that $5$ own a Pumpkin phone. Calculate an approximate $95\%$ confidence interval for the proportion of students at Florence’s college who own a Pumpkin phone.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct hypotheses are $H_0:p=0.25$, $H_1:p<0.25$” …