The UMUC Daily News reported that the color distribution for plain M&M's was: 40%brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a randomsample of 100 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.
Brown = 42
Yellow = 18
Orange = 15
Green = 7
Tan = 18
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 distribution is correct? Justify your answer.