3. Suppose the makers of M&M candies give the followingaverage percentages for the mix of colors in their bags of plainchocolate M&M's. Stated Distribution of Colors Brown Yellow RedOrange Green Blue Percent 30% 20% 20% 10% 10% 10% Now, you randomlyselect 200 M&M's and get the counts given in the table below.You expected about 20 blues but only got 10. You suspect that themaker's claim is not true. Observed Counts by Color (n = 200) BrownYellow Red Orange Green Blue Count 66 35 44 22 23 10 The Test: Testwhether or not the color of M&M's candies fits the distributionstated by the makers (Mars Company). Conduct this test at the 0.05significance level. (a) What is the null hypothesis for this testin terms of the probabilities of the outcomes? H0: pbrown = pyellow= pred = porange = pgreen = pblue = 1/6 H0: At least one of theprobabilities doesn't fit the company's statement. H0: pbrown =0.30, pyellow = 0.20, pred = 0.20, porange = 0.10, pgreen = 0.10,and pblue = 0.10. H0: The probabilities are not all equal to 1/6.(b) What is the value of the test statistic? Round to 3 decimalplaces unless your software automatically rounds to 2 decimalplaces. χ2 = (c) Use software to get the P-value of the teststatistic. Round to 4 decimal places unless your softwareautomatically rounds to 3 decimal places. P-value = (d) What is theconclusion regarding the null hypothesis? reject H0 fail to rejectH0 (e) Choose the appropriate concluding statement. We have proventhat the distribution of candy colors fits the maker's claim. Thedata suggests that the distribution of candy colors does not fitthe maker's claim. There is not enough data to suggest that thedistribution of candy colors is different from what the makersclaim.
