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