All work must be shown. Failure to do so will result in a grade of \"0". The M&M candies manufacturer claims that its bags of plain M&M candies have the following distribution of colors: 20% red. 30% green. 15% yellow and 35% brown. A bag was purchased. and the number of each color was recorded in the table below. Color Red Green Yellow I Brown Count 31 15 l? 37 (a) Is there sufcient evidence at 5% signicance level to support the manufacturer's claim? (b) Consider the number of red colored M&M's and brown colored M&M's in a new batch. Test the claim that there is 10% less red colored M&M's than brown colored M&M's in its bags of plain M&M candies ato = 0.05. where at,\" 2 32mm\"! 2 100, xmow" = 36, ann = 100. (c) Which of the following statementts} isr'are correct? I. A test for the difference between two proportions can he performed using the chi-square test. 11. \"then testing for independence in a contingency table with 3 rows and 4 columns, there are 7 degrees of freedom. [I]. Chisquare goodnessvoft test is always a onevtailed test. IV. If we use the Chisquare test of independence, we must assume that there are at least 5 observed frequencies in each cell of the contingency table