# Hypothesis testing

## Hypothesis testing

A company claims that it receives emails at a mean rate of 2 every 5 minutes.

(a) Give two reasons why a Poisson distribution could be a suitable model for the     number of emails received.

(b) Using a 5% level of significance, find the critical region for a two-tailed test of the
hypothesis that the mean number of emails received in a 10 minute period is 4. The
probability of rejection in each tail should be as close as possible to 0.025

(c) Find the actual level of significance of this test.

To test this claim, the number of emails received in a random 10 minute period was
recorded.

During this period 8 emails were received.

(d) Comment on the company’s claim in the light of this value. Justify your answer.

During a randomly selected 15 minutes of play in the Wimbledon Men’s Tennis
Tournament final, 2 emails were received by the company.

(e) Test, at the 10% level of significance, whether or not the mean rate of emails received by the company during the Wimbledon Men’s Tennis Tournament final is lower than the mean rate received at other times. State your hypotheses clearly.

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