Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
A nationwide survey indicates that $95\%$ of year 12 students use social media. Arvin thinks that the proportion of year 12 students at his college who use social media is below the national percentage. He takes a random sample of $20$ students from his college and records how many use social media. He then carries out a test at the $2\%$ significance level.
(a)[4]
Find the rejection region for this test.
(b)[1]
Find the probability of a Type I error occurring.
(c)[3]
Jimmy thinks that the actual percentage at Arvin’s college is $70\%$. Assuming that Jimmy is correct, find the probability of a Type II error.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Try to calculate $P(X \le n)$ for $n \le 20$ using $B(20, 0.95)$.” …