6. As a budding data scientist with much promise, a person who is considering running as a Member of Parliament (MP) for a certain riding hires you to conduct some polling. Due to the time investment and the cost (time and finances) of a political campaign, you decide to take a random sample of n = 50 voters who live within this particular riding. Each are to be asked "if they would support this particular candidate if they ran as a reprsentative for Party X in the next federal election". If your polling/sampling suggests that they will receive at least 45% of the vote, then you will council this person to \"run for office". In your preliminary statistical work, you have decided that there is enough statistical evidence to support the "mimimum of 45%"-claim if out of n = 50 randomly chosen voters, at least 20 indicate they will vote for this candidate if they run. a. State the statistical hypotheses. b. Compute the value of (1 used in your derivation of the decision rule. c. What if the candidate were to receive 42% of the vote. Compute the probability that you will conclude they should run for office. Interpret the meaning of this probability. d. Repeat for (c) for these values of p:p = 0.41, p = 0.40, p = 0.39, p = 0.38, p = 0.35 and p = 0.30. For each differeing value of P, compute the probability computed in part {c}. THEN, create a plot with the differing values ofP on the X-axis and the probabilties computed on the Yaxis. e. What does your plot/graph in part (d) tell you about your statistical test? How can you improve your test? Provide some suggestion{s), reasoning why each would make your statisical test better