The UMUC Daily News reported that the color distribution for

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 random sample 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.
Color
Brown
Yellow
Orange
Green
Tan
Number
42
21
12
7
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 critical 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.

Solution

A.

Ho: The said distribution is the distribution followed by the plain M&M\'s.

Ha: The said distribution is not the distribution followed by the plain M&M\'s.

B.

Writing out an expected value (E) table vs observed (O)

O   E
42   40
21   20
12   20
7   10
18   10

As

chi^2 = Sum[(O - E)^2 / E]

Then

chi^2 = 10.65 [ANSWER, B]

****************

C.

df = a - 1

As a = 5, df = 4.

Thus, using technology,

P value = 0.03079232 [ANSWER]

Also, the critical value at 0.05 significance using technology/table is

chi^2(crit) = 9.487729037 [ANSWER]

******************

D.

As Pvalue < 0.05, then WE REJECT THE NULL HYPOTHESIS: there is NO SUFFICIENT EVIDENCE that the said color distribution is correct.