Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
A machine is meant to generate random digits. Bob believes that the machine is biased and that the chance of producing the digit $0$ is smaller than $\frac{1}{10}$. To check this, he counts how many times the digit $0$ appears in $30$ digits produced by the machine. He carries out a test at the $10\%$ significance level.
(a)[1]
State appropriate null and alternative hypotheses.
(b)[4]
Find the rejection region for this test.
(c)[1]
State the probability associated with a Type I error.
(d)[3]
Find the probability associated with a Type II error.
(e)[1]
Explain what a Type II error means in this context.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct hypotheses are $H_0:P(0)=\frac{1}{10}$, $H_1:P(0)<\frac{1}{10}$” …