Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Previously, for Laxmi’s journey to college, the time taken in minutes had a mean of $32.5$ and a standard deviation of $3.1$. After she changes her route, Laxmi wants to check whether the mean time has gone down. She records the journey times for a random sample of $50$ trips and obtains a sample mean of $31.8$ minutes. Assume that the standard deviation stays the same.
(a)[5]
Carry out a hypothesis test, at the $8\%$ significance level, to check whether Laxmi’s mean journey time has decreased.
(b)[5]
At a later stage, Laxmi carries out a similar test with the same hypotheses, using another random sample of size $50$ and the $8\%$ significance level. If the population mean is now $31.5$, find the probability of a Type II error.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Hypotheses correctly given as $H_0:\mu=32.5$, $H_1:\mu<32.5$” …