4. [10 pts] It is claimed that 42% of US college graduates had a mentor in college. For a sample of college graduates in Colorado, it was found that 502 out of 1045 had a mentor in college. Test the claim that the proportion of college grads in Colorado who had a mentor is greater than that of all US college grads. a. State the null and alternative hypotheses. b. Check the Central Limit Theorem. c. Set up a sampling distribution of proportions. d. Find the p-value. e. State your conclusion of the test. 5. [6 pts] A soccer player makes 78% of the penalty kicks that she shoots. a. If she shoots 10 penalty kicks one season, what's the probability that she makes all 10? b. If she shoots 10 penalty kicks one season, what's the probability that she makes at most 6? c. If she shoots 10 penalty kicks one season, what's the probability that she makes at least 8? 6. [10 pts] Below are pairings of the cost of an airline ticket that was purchased 30 days in advance versus one day in advance. 30 Days 244 260 264 264 278 318 280 One Day 456 614 567 943 628 1088 536 a. What is the correlation coefficient? b. Describe the association using the correlation coefficient. c. Find the least squares regression line d. Find the best predicted cost of a ticket purchased one day in advance, given that the cost of the ticket is $300 if purchased 30 days in advance of the flight