Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The tree height $H$, measured in metres, for mature trees of a particular variety follows a normal distribution with standard deviation $0.67$. To test whether the population mean of $H$ is greater than $4.23$, the heights of a random sample of 200 trees are measured.
(a)[1]
Write down appropriate null and alternative hypotheses for this test.
(b)[3]
The sample mean height, $\bar{h}$ metres, for the 200 trees is obtained and the test is performed. The null hypothesis is rejected at the 5% significance level. Determine the set of possible values of $\bar{h}$.
(c)[1]
Ajit stated, "In (b) we had to assume that $\bar{H}$ is normally distributed, so it was necessary to use the Central Limit Theorem." Explain whether you agree with Ajit.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the hypotheses as $H_0: \mu=4.23$, $H_1: \mu>4.23$.” …