Mathematics 9709 · AS & A Level · Hypothesis testing

Hypothesis testing — practice question

Earlier, the yearly quantity of wheat produced per farm by a large number of similarly sized farms in one region had a mean of $24.0$ tonnes and a standard deviation of $5.2$ tonnes. Last summer a new fertiliser was applied on all the farms, and it was expected that the mean quantity of wheat produced per farm would exceed $24.0$ tonnes. To check whether this was correct, a scientist recorded the amounts of wheat produced by a random sample of $50$ farms last summer. He found that the sample mean was $25.8$ tonnes.
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State the necessary assumption, and carry out the test at the $1\%$ significance level.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Assume that the standard deviation remains $5.2$.

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