Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Anjan’s Monday commute to work, measured in minutes, has a mean of $38.4$ and a standard deviation of $6.9$.
(a)[5]
Work out the probability that the mean journey time for a random sample of $30$ Mondays lies between $38$ and $40$ minutes.
(b(i))[1]
State, with a reason, whether Anjan should use a one-tail or a two-tail test.
(b(ii))[5]
Carry out the test at the 10% significance level.
(b(iii))[1]
Explain whether it was necessary to use the Central Limit Theorem in part (b)(ii).
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use continuity correction correctly when standardising, for example $\dfrac{40-38.4}{6.9/\sqrt{30}}$ or $\dfrac{38-38.4}{6.9/\sqrt{30}}$.” …