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Use an approximating distribution to carry out the test at the $2.5\%$ significance level to determine whether $\lambda$ has increased.
Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The counts of customers entering a particular shop from 9.00 am to 10.00 am have the distribution $\text{Po}(\lambda)$. In the past, the value of $\lambda$ was $5.2$. After some new advertising, the manager wants to check whether $\lambda$ has gone up. He takes a random sample of $20$ days and finds that the total number of customers who visited the shop between $9.00$ am and $10.00$ am on those days is $125$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct hypotheses, e.g. $H_0:\lambda=104$ (or $5.2$), $H_1:\lambda>104$ (or $5.2$)” …
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