Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Earlier, 1/4 of people applying for jobs at a particular firm possessed first-class degrees. The job description is then altered, and a director of the firm thinks that, on average, the proportion of applicants with first class degrees has fallen.
In the month after the alteration, there were 35 job applicants, and $r$ of these had first-class degrees. The firm carried out a hypothesis test at the $4\%$ significance level to check the director’s view.
(a)[6]
Apply a binomial distribution to determine the greatest value of $r$ that would give enough evidence that the director’s belief is right.
(b)[2]
Explain the meaning of a Type I error in this context, and state the probability of a Type I error.
(c)[2]
If the proportion of job applicants with first class degrees this year is actually $0.05$, find 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: “Identify the binomial model $B(35,0.25)$” …