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Question 20 22 pts Be sure to show all work for full credit. In October 2020, the non-profit organization Twin Cities in Motion hosted the 2020 Medtronic Twin Cities Marathon Weekend event. There were four races in this event: Marathon, 10-mile run, 10-km run, and 5-km run. This year, all races were conducted virtually, that is, each runner ran the distance at their own time and their own location, and submitted the finishing time to the event organizer. A total of over 3,200 unique runners had participated in the races. For parts 1 through 3, consider the following scenario: Among the 333 participants in the 10-km running race, 78 were from outside Minnesota; among the 428 participants in the 5-km running race, 74 were from outside Minnesota. Assume that these runners represent random samples from all virtual 10-km runs and virtual 5-km runs sponsored by Twin Cities in Motion, respectively, and assume that the samples are independent. Let p10 and p5 denote the population proportions of participants of all virtual 10-km runs and virtual 5-km runs sponsored by Twin Cities in Motion that are from outside Minnesota, respectively. 1. (2 points) State and check the assumptions for constructing a 99% confidence interval for p10 - P5. 2. (5 points) Regardless of your answers to part 1, supposed that the assumptions have been met. Construct and interpret a 99% confidence interval for p10 - P5. The following R codes might be helpful: at(0. 005, df=332, lower=F) = 2.590 at(0. 005, df=427, lower=F) = 2.587 qnorm(0. 005, lower=F) = 2.575 3. (3 points) What is the standard error for testing whether p10 is significantly greater than p5 at the significance level a = 0.01? You DO NOT need to conduct the actual hypothesis test