Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The weekly profit, measured in dollars, for a particular firm follows a normal distribution. Previously, the weekly profit had distribution $N(736, 26^2)$. After a change in management, the mean weekly profit over 35 randomly selected weeks is $725$.
(a)[6]
With the necessary assumption stated, test at the $2\%$ significance level whether the mean weekly profit has decreased.
(b)[1]
State the probability of making a Type I error.
(c)[5]
Given that the mean weekly profit is now actually $718$, find the probability of a Type II error.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Take the standard deviation to remain $26$ (unchanged)” …