Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Birgitte has a six-sided dice. She thinks that the dice may be biased, with the probability, $p$, of getting a six on a single throw being less than $\frac{1}{6}$. She rolls the dice 30 times and gets a six on exactly 2 throws.
(a)[5]
Test Birgitte’s suspicion by using a binomial distribution at the 5% significance level.
(b)[2]
At a later stage, Birgitte performs a similar test at the 5% significance level, again using another 30 throws of the dice. Calculate the probability of a Type I error.
(c)[3]
If the true value of $p$ is $0.02$, calculate the probability of a Type II error.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Hypotheses stated as $H_0:p=\frac{1}{6}$, $H_1:p<\frac{1}{6}$” …