Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
A researcher has recorded the time, $T$ seconds, needed by adults to finish a questionnaire. The findings for a random sample of $60$ adults who completed the questionnaire this year are summarised as follows: $n = 60$, $\sum t = 3678$, $\sum t^2 = 226313.36$.
(a)[3]
Find an unbiased estimate of $E(T)$, and show that an unbiased estimate of $\mathrm{Var}(T)$ is $14.44$.
(b)[5]
In the past, the population mean time was $62.4$ seconds. Test at the $2\%$ significance level whether the population mean time for this year is less than $62.4$ seconds.
(c)[1]
State, with a reason, whether using the Central Limit Theorem was required in your answer to part (b).
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Sample mean $\hat\mu=61.3=\dfrac{3678}{60}=613/10$” …