Mathematics 9709 · AS & A Level · Hypothesis testing

Hypothesis testing — practice question

A website records an average of $\mu$ hits each hour. In the past, the value of $\mu$ was 14.4. After some improvements, the owner wants to check whether $\mu$ has gone up. He randomly selects a 10-minute interval and records 6 hits in that interval. Assume that the number of hits the website gets in any fixed time period follows a Poisson distribution.
(a)[6]

Carry out the test using the 2.5% significance level.

(b)[2]

Explain whether a Type I error, a Type II error, or both could have been made when carrying out the test.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: State the hypotheses as $H_0:\lambda=2.4$ (or $\mu=14.4$) and $H_1:\lambda>2.4$ (or $\mu>14.4$)

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