2. A student in the STATS 210 class writes down the following for answering a question related to hypothesis testing in the case when the only observation that is available for the random variable X is x. X ~ Binomial (20, p), 0 x) = 2(1 P(X x 1)) = 2(1 Fx(x 1)) = 2 (1pbinom(x 1, 20, 0.2)) Answer the following questions: (a) Provide a short justification in which to explain why the equations above can be used in the case when x = 8. For x = 8, run the command in R for computing the p-value. Quote your answer to 5 decimal places. (b) Give an example of a value for x, 0 < x < 20, such that the p-value is smaller than the one computed in part (a). Justify your selection. Run the necessary command in R in order to confirm that p-value computed with the value of x that you propose is smaller than the p-value calculated in part (a). B