Mathematics 9709 · AS & A Level · Hypothesis testing

Hypothesis testing — practice question

The areas, $X\;\text{cm}^2$, of petals from one species of flower have mean $\mu\;\text{cm}^2$. It was previously established that $\mu = 8.9$. After a change in climate, a botanist states that the mean is not still $8.9$. The areas of a random sample of $200$ petals from this species are recorded, and the data are summarized by $\Sigma x = 1850$, $\Sigma x^2 = 17\,850$.
(main)[8]

Test whether the botanist’s claim is supported at the $2.5\%$ significance level.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct sample mean $\hat{\mu}=\frac{1850}{200}=9.25$.

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