Question: 5. In order to test whether a certain coin is fair, it is tossed ten times and the number of heads (X) is counted. Let

5. In order to test whether a certain coin is fair, it is tossed ten times and the number of heads (X) is counted. Let p be the \"head probability". We wish to test the null hypothesis: p = 0.5 against the alternative hypothesis: :0 > 0.5 at a significance level of 5%. (a) Suppose we will reject the null hypothesis when X 3 11. Find the value of h. Ci [6 marks] (13) What is the probability of committing a type I error? 0. 0 I l [3 marks] ((3) What is the probability of committing a type 11 error if the true value of p is 0.75? 057 g [5 marks] [Total: 14 marks]

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