3 Each year Crowmouth running club stages a marathon. From previous years it is known that 17% of the people who enter will complete the marathon in under 3 hours. This year, the start time of the race has changed. A sports scientist claims that as a result, the percentage of entrants who finish in under 3 hours will increase. There will be 500 people competing in this year's race. The number finishing in under 3 hours is to be modelled using the binomial distribution. (a) Give one reason why the binomial distribution might not be appropriate. Assuming that the binomial distribution is appropriate, a hypothesis test at the 10% significance level is to be used to test the scientist's claim. (b) Write down the hypotheses that should be used. (c) Find the critical region for the test and state the actual significance level that the test will use. (d) Explain why a test value that is not in the critical region will not disprove the scientist's claim.

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