The UMUC Daily News reported that the color distribution for plain M&M's was: 35% brown, 30% yellow, 15% orange, 10% green, and 10% tan . Each piece of candy in a random sample of 200 plain M&M's was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work and justify your answer.
Color Brown Yellow Orange Green Tan
Number 80 45 30 30 15
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that the published color distributi on is correct? Justify your answer.