1. In the Whoville criminal justice system, the Whoville Grand Jury (WGJ) determines which suspected criminals will be tried for their suspected crimes, and which will not. As such, it wields a lot of power. By the Whoville constitution (article 5e), the 31 members of the WGJ are to be selected at random, once a year, from the pool of all eligible adult Whos. Any Who selected for WGJ service may request to be exempted for reasons of economic hardship or religious belief, and if their request is found to have merit, they are replaced by another eligible adult Who. Once their year-long service on the WGJ is complete, Whos are moved to the ineligible list for 10 years. Cindy Lou Who (CLW) suspects that the selection process for the WGJ is not as random as it should be. She believes that the orange marble clan (to which she belongs) has been systematically under- represented in Whoville Grand Juries for many years. To substantiate her beliefs, CW decides to use a y? goodness-of-fit test to compare the numbers of each marble clan that have served on the WGJ to the expected numbers. The test will be based on the proportions of each clan in Whoville, and the hypothetical randomness of the selection process. CLW chooses a 5% significance level. From the latest census data, it is known that the proportions of the marble clans in Whoville are Red clan- 32%. . Blue clan- 38%. Green clan - 17%. Orange clan - 9%. . Other, or no clan- 4%. From the records of the WGJ, the numbers of each clan that have served on the WGJ in the past 10 years are Red clan 117. . Blue clan 126. . Green clan 42. . Orange clan 16. Other, or no clan 9. (a) (2 pts) Explain briefly why the conditions for a y? goodness-of-fit test are satisfied. (b) (2 pts) Find the null-hypothetical expected numbers of marble clan members (from each category) on the WGJ for the past 10 years, based on the Ho-assumption that Whos are selected randomly for the WGJ. (c) (2 pts) Find the x? statistic for CW's Lest, and the corresponding p-value. Show your weak and for explain your answerf. (d) Summarize your conclusions: i. (1 pt) Is the statistical evidence strong enough to reject the null hypothesis that the proportions of WGJ members At (he distribution of marble clan membership in Whoville? li. (3 pts) Do the data support CW's claim of systematic bias against the orange marble clan in the random selection process of WGJ members? Explain your answer, taking into consideration all of the given information