a) Binomial Table A1 is required to determine the exact probability of a Type I error, and it can be obtained as follows:Let p0 be the null hypothesis value, which is θ5 in this case.Let p1 be the alternative hypothesis value, which is greater than θH in this case.n is the sample size, which is 10 in this case.Using these values in the Binomial Table A1, we can find the probability of a Type I error.To determine the probability of a Type I error for this question using Binomial Table A1, follow the given steps:Step 1: Find the probability of the critical region using the given critical value:B ≥ 8. This means that the critical region is {8, 9, 10}.Thus, the probability of the critical region is:P(B ≥ 8) = P(B = 8) + P(B = 9) + P(B = 10)Step 2: Use the Binomial Table A1 to find the exact probabilities of each of these values:Here, p0 = θ5 = 0.5 and p1 > θH. Therefore, we need to use the row corresponding to n = 10 and column corresponding to p = 0.5.From the table, we can find:P(B = 8) = 0.044, P(B = 9) = 0.010, and P(B = 10) = 0.001Therefore, the probability of a Type I error is:P(B ≥ 8) = 0.044 + 0.010 + 0.001 = 0.055 (rounded to three decimal places)b) The p-value is the probability that B ≥ bobs given that H0 is true, and it can be found using the Binomial Table A1.To find the p-values for each of the given values of bobs = 5, 6, 7, 8, 9, 10, we can use the following formula:p-value = P(B ≥ bobs | H0 is true) = P(B = bobs) + P(B = bobs + 1) + ... + P(B = n)Here, n = 10 is the sample size, and θ5 = 0.5 is the null hypothesis value. Therefore, we need to use the row corresponding to n = 10 and column corresponding to p = 0.5 in the Binomial Table A1.Using the table, we can find the probabilities of B = bobs, B = bobs + 1, ..., B = n for each value of bobs = 5, 6, 7, 8, 9, 10. Then, we can add these probabilities to find the p-values for each value of bobs as shown below:p-value when bobs = 5:P(B = 5) + P(B = 6) + ... + P(B = 10) = 0.246 + 0.205 + 0.115 + 0.044 + 0.010 + 0.001 = 0.621 (rounded to three decimal places)p-value when bobs = 6:P(B = 6) + P(B = 7) + ... + P(B = 10) = 0.205 + 0.115 + 0.044 + 0.010 + 0.001 = 0.375 (rounded to three decimal places)p-value when bobs = 7:P(B = 7) + P(B = 8) + ... + P(B = 10) = 0.115 + 0.044 + 0.010 + 0.001 = 0.170 (rounded to three decimal places)p-value when bobs = 8:P(B = 8) + P(B = 9) + P(B = 10) = 0.044 + 0.010 + 0.001 = 0.055 (rounded to three decimal places)p-value when bobs = 9:P(B = 9) + P(B = 10) = 0.010 + 0.001 = 0.011 (rounded to three decimal places)p-value when bobs = 10:P(B = 10) = 0.001Therefore, the p-values for bobs = 5, 6, 7, 8, 9, 10 are 0.621, 0.375, 0.170, 0.055, 0.011, and 0.001 respectively (rounded to three decimal places).