Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
A researcher examined a magazine piece that said boys aged $1$ to $3$ prefer green rather than orange. It claimed that, if a green cube and an orange cube are offered to play with, a boy is more likely to select the green cube. The researcher does not agree with this claim. She thinks boys in this age range are equally likely to choose either colour. To test this belief, the researcher carried out a hypothesis test at the $5\%$ significance level. She gave a green cube and an orange cube to each of $10$ randomly selected boys aged $1$ to $3$, and noted the number, $X$, of boys who chose the green cube. Of the $10$ boys, $8$ boys chose the green cube.
(a(i))[1]
If the researcher’s belief that each colour cube is equally likely to be chosen is taken as true, a student correctly finds that $P(X = 8) = 0.0439$, correct to $3$ significant figures. He then says that, because this is less than $0.05$, the null hypothesis should be rejected. Explain why this is wrong.
(a(ii))[5]
Carry out the test for the researcher’s claim that either colour cube is equally likely to be chosen.
(b)[1]
Another researcher says that a Type I error was made in carrying out the test. Explain why this cannot be true.
(c)[2]
A similar test, at the 5% significance level, was later carried out using 10 other randomly selected boys aged 1 to 3. Find the probability of a Type I error.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Identify that $P(X \ge 8)$ is required” …