MEM's Color Distribution: Suppose the makers of MBIM candies give the following average percentages for the mix of colors in their bags of plain chocolate M&M's. Stated Distribution of Colors Brown Yellow Red Orange Green Blue Percent 30% 20% 20% TECH: 10% 10% Now, you randomly select 200 Mimi's and get the counts given in the table below. You expected about 20 blues but only got 12. You suspect that the maker's claim is not true. Observed Counts by Color (n = 200} Brown Yellow Red Orange Green Blue Count 63 29 50 18 23 12 111.3 Test: Test whether or not the color of MSLM's candies ts the distribution stated by the makers (Mars Company). Conduct this test at the 13.01 significance level. (a) What is the null hypothesis for this test in terms of the probabilities of the outcomes? 0 Ho: At least one of the probabilities doesn't fit the company's statement. 0 H0: The probabilities are not all equal to 1,.I'6. O Ho: pbmwn = 6.30, smug\" = 0.29.. Pred = 0.20,. ponge = 0.1!}, agree" = 0.10, and pblue = 0.10. O HO: pbrown = pyellow = precl = pomnge = pgreen = phlue = 11"5 (b) What is the value of the test statistic? Round to 3 decimal places unless your software automacaliy rounds to 2 decimal planes. (1:) Use software to get the Pyalue of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places. P-value = |:| (d) What is the conclusion regarding the null hypothesis? 0 reject HO O fail to reject Ho (e) Choose the appropriate conduding statement. 0 We have proven that the distribution of candy colors ts the maker's claim. 0 The data suggests that the distribution of candy colors does not t the maker's claim. 0 There is not enough data to suggest that the distribution of candy colors is different from what the makers claim