Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
On Mondays, Anjan’s journey-to-work time, measured in minutes, has mean $38.4$ and standard deviation $6.9$.
(a)[5]
Find the probability that the mean journey time for a random sample of $30$ Mondays is 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 $\text{b(ii)}$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate standardisation, e.g. $\frac{40-38.4}{6.9/\sqrt{30}}=1.270$.” …