Problem 4.Before the last presidential debates, 50% of registered votes indicated they were planning to vote for the incumbent president. In a recent poll of 1200 registered voters after the debates, 636 indicated they are planning to vote for the incumbent president. Has there been asignificantincreasein the proportion of registered voters who are planning to vote for the incumbent president?

Answer question 4.1 to question 4.12 regarding problem 4.

Question 4.1. The sample proportion in problem 4 follows which of the following probability distribution?

Group of answer choices

Question 4.2. What is the standard deviation of sample proportionin order to come up an interval estimation of the proportionusing the sample information in problem 4 (i.e., if we are not going to do any hypothesis test and we do know the last presidential debate result)?

Question 4.3. If we would like to come up a confidence interval estimation of proportion in problem 4 with 95% confidence level, what would be the margin of error?

Question 4.4. If we would like to come up a confidence interval estimation of proportion in problem 4with 95% confidence level, what would be the upper bound of the interval?

Question 4.5. If we would like to come up a confidence interval estimation of proportion in problem 4 with 95% confidence level, what would be the lower bound of the interval?

Question 4.8. What are the test statistics for problem 4?

Question 4.9. What is the p-value of the test statistics for problem 4?

Question 4.10. If = 0.01 is used, what is the critical value? (for multiple values, enter the positive one)