9 It is desired to test whether the average amount of sleep obtained by school pupils in Year 11 is 8 hours, based on a random sample of size 64. The population standard deviation is 0.87 hours and the sample mean is denoted by \(\bar { H }\). The critical values for the test are \(\bar { H } = 7.72\) and \(\bar { H } = 8.28\).

1. State appropriate hypotheses for the test, explaining the meaning of any symbol you use.
2. Calculate the significance level of the test.
3. Explain what is meant by a Type I error in this context.
4. Given that in fact the average amount of sleep obtained by all pupils in Year 11 is 7.9 hours, find the probability that the test results in a Type II error. \section*{THERE ARE NO QUESTIONS WRITTEN ON THIS PAGE.}