(a)[4]
Calculate the probability of a Type I error.
(b)[1]
State the rejection region for this test.
(c)[1]
Laxmi finds exactly 2 households in her sample with more than 4 people. Explain why it is impossible for Laxmi to make a Type II error.
Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
It is given that 20% of households in one country have more than 4 people. Laxmi thinks that the proportion in her town is below 20%. She takes a random sample of 40 households in her town and records how many have more than 4 people. She then performs a test at the 2.5% significance level with a binomial distribution.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$P(X\le2)=0.8^{40}+40(0.8)^{39}(0.2)+\binom{40}{2}(0.8)^{38}(0.2)^2$” …
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