Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Previously, the time taken, in hours, for one particular train journey had mean $1.40$ and standard deviation $0.12$. After new signals were introduced, it is necessary to test whether the mean journey time has fallen.
(a)[1]
State what a Type II error means in this situation.
(b)[5]
The mean time from a random sample of $50$ journeys is $1.36$ hours. If the standard deviation of journey times is still $0.12$ hours, test at the $2.5\%$ significance level whether the population mean journey time has decreased.
(c)[2]
State, with a reason, which of Type I or Type II errors may have been made in the test in part (b).
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Conclude that the (mean) journey time has not decreased although, in reality, it has” …