(a)[3]
Calculate unbiased estimates of the population mean and variance of the revised journey time.
(b)[5]
Test, at the $5\%$ significance level, whether the population mean time has decreased.
Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Before the one-way system was brought in, Freda’s mean time for a certain daily trip was $39.2$ minutes. Now she wants to check whether the mean time for that journey has gone down. She records the times, $t$ minutes, for 40 journeys chosen at random and summarises them as follows: $n = 40$, $\sum t = 1504$, $\sum t^2 = 57760$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Mean estimate $\mu = 37.6$ (or $\frac{1504}{40}$ or $\frac{188}{5}$).” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI