Be sure to show your work for problems that require calculation. 1. A USA Today story reported the college students living situation reflects the following percentages: Parents' home Campus housing 26% Off-campus rental 18% Own off-campus housing 18% Does the living situation distribution of UT Austin students differ from the national distribution? (7 pts) Use a critical value of 7.815. A random sample of UT students resulted in the following information: Parents' home Campus housing Off-campus rental 168 Own off-campus housing 140 What are the null and alternate hypotheses for this test? (1 pt) Calculate the expected counts for this distribution. (1 pt) What are the conditions for this test? Are they met? Why or why not? {1 pt) Perform the chi-square test for goodness of t to answer the question above. Show your work. (2 pt) e. Write an appropriate conclusion for this test. (2 pts) 0.5159: 2. Each of the Skittles colors are expected to be equally represented in a package of the candies. lfa student found the following counts in a case of Skittles, did the distribution match the expected distribution? Use a critical value of 9.483. {5.75 pts} 3. Calculate the expected counts for this distribution. {1.25 pts} b. Perform the chi-square test for goodness of fit to answer the question above. {2 pts) c. Write an appropriate conclusion for this test. {2 pts} 3. Researchers wanted to know if the females are pickier in their ratings of the quality of the restrooms than males; or, ifthe quality of the facilities rating is independent of gender. A survey was conducted of 100 randomly selected travelers who used a certain gas station restroom. Here are the results. {3.25 pts} l l Quality of Restroom Facility l Above Average Average Below Average Total a. What percent of the respondents were female? b. What percent of the respondents said the restrooms were above average? c. What percent of the respondents were females who said the restroom was below average? What percent of males said the restrooms were average? What percent of respondents who rated the restrooms below average were male? Find the marginal distribution (percentages) for sex. Find the marginal distribution (percentages) for quality of restroom facility. Find the conditional distribution (percentages) for quality of restroom facility for females. anyone