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Assuming that the standard deviation stays at $2.6\,$cm, carry out a test at the $2\%$ significance level to decide whether the mean length has fallen.
Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
Earlier, the mean length of a specific variety of worm was $10.3\,$cm, and the standard deviation was $2.6\,$cm. After a change in climate, it is believed that the mean length of this variety of worm has fallen. A random sample of $100$ worms of this variety is taken, and the sample mean is $9.8\,$cm.
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 in the form $H_0: \mu = 10.3$, $H_1: \mu < 10.3$” …
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