Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Previously, Jenny’s mean time for her morning run was 28.2 minutes. She has done some additional training and wants to check whether her mean time has decreased. After the training, Jenny takes a random sample of 40 morning runs. She decides that if the sample mean run time is below 27 minutes, she will conclude that the training was effective. You may assume that, after the training, Jenny’s run time has a standard deviation of 4.0 minutes.
(a)[1]
State suitable null and alternative hypotheses for Jenny’s test.
(b)[3]
Find the probability that Jenny makes a Type I error.
(c)[2]
Jenny obtained a sample mean run time of 27.2 minutes. Explain briefly whether she could make a Type I error or a Type II error or both.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “States $H_0: \mu = 28.2$ and $H_1: \mu < 28.2$” …