Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Earlier, Laxmi’s journey to college, measured in minutes, had a mean of $32.5$ and a standard deviation of $3.1$. After altering her route, she wants to check whether the mean travel time has fallen. She records her journey times for a random sample of $50$ journeys 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 determine whether Laxmi’s mean journey time has decreased.
(b)[5]
Later, Laxmi carries out a similar test with the same hypotheses, at the $8\%$ significance level, using another random sample of size $50$. 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 stated correctly for population mean $\mu$” …