Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Previously, the time in minutes that students needed to finish a particular challenge had a mean of $25.5$ and a standard deviation of $5.2$. A different challenge is now set, and it is anticipated that, on average, students will need less than $25.5$ minutes to finish it. A random sample of $40$ students is taken, and the sample mean time for the new challenge is $23.7$ minutes.
(a)[5]
Given that the standard deviation of the time for the new challenge is $5.2$ minutes, test at the $1\%$ significance level whether the population mean time for the new challenge is below $25.5$ minutes.
(b)[1]
State, with a reason, whether it is possible that a Type I error was made in the test in part (a).
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write the hypotheses as $H_0:\mu=25.5$, $H_1:\mu<25.5$” …