Hi, please show me how to solve the question below without using excel formulas. Please round all answers to four decimal places and show all calculation steps clearly so I can understand the process. Thank you

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 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 at n= 0.05, where xred = 32,1zmd = 100, xbmwn = Bombmwn = 100. (c) Which of the following statement(s) is/ are correct? I. A test for the difference between two proportions can be performed using the chi-square test. 11. When testing for independence in a contingency table with 3 rows and 4 columns, there are 7 degrees of freedom. III. Chi-square goodness-oft test is always a one-tailed test. IV. If we use the Chi-square test of independence, we must assume that there are at least 5 observed frequencies in each cell of the contingency table