1. (15 points) For the first time ever in 2022, Major League Baseball is using humidors to store baseballs at all thirty ballparks. The idea is that if all the baseballs across the league are stored at the same level of humidity, then the performance of the baseballs will be more consistent regardless of the climate of the city where the ballparks are located. Some people claim that storing all the balls in humidors will reduce the exit velocity, which is the speed at which balls are hit off the bat. Suppose that a simple random sample of 50 baseball players from 2021 yielded a mean exit velocity of 89.4 feet per second with a standard deviation of 5.9 feet per second, and a simple random sample of 40 baseball players from 2022 yielded a mean exit velocity of 88.7 feet per second with a standard deviation of 5.2 feet per second. Test the claim at the 5% level of significance. (Hint: the degrees of freedom are df = 87.13628156). 2. {15 points) The superintendent of a school district wishes to determine if there is a difference in the proportion of kindergartners who went to preschool for two different elementary schools. In a simple random sample of 95 kindergartners attending School A, 42 of them had attended preschool. In a simple random sample of 88 kindergartners attending School B, 29 of them had attended preschool. At the 5% significance level, test the claim that the proportion of kindergartners who went to preschool is different at these two elementary schools. 3. (15 points) An auto shop claims that their tune-up service increases gas mileage. Fourteen randomly selected cars had their gas mileage measured before and after the tune-up, with the results (in miles per gallon) displayed in the table below. Test the auto shop's claim at the 1% significance level. Assume that the differences are normally distributed with no outliers. Hint: If we calculate the differences as After - Before, then H1: Ma > 0. If we calculate the differences as Before - After, then H1: Ma