Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
For apples taken from a particular farm, the masses in grams have mean $\mu$ and standard deviation $5.2$. The farmer states that $\mu$ is $64.6$. A quality control inspector argues that $\mu$ is actually below $64.6$. To check this claim, a random sample of $100$ apples is selected from the farm.
(a)[5]
The sample mean mass for the $100$ apples is $63.5\text{ g}$. Perform the test at the $2.5\%$ significance level.
(b)[5]
A second test of the same hypotheses at the $2.5\%$ significance level is then carried out, using another random sample of $100$ apples from the same farm. If $\mu$ is actually $62.7$, calculate 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: “State the hypotheses $H_0:\mu=64.6$, $H_1:\mu<64.6$” …