18. The UMUC Daily News reported that the color distribution for plain M&Ms was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan.Each piece of candy in a random sample of 100 plain M&Ms 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- 21

Orange- 12

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