Question

Are all colors equally likely for Milk Chocolate M&M's? Data collected from a bag of Milk Chocolate M&M's are provided.

Blue            Brown        Green          Orange       Red          Yellow

110                   47               52                 103            58                50

a. State the null and alternative hypotheses for testing if the colors are not all equally likely for Milk Chocolate M&M's.

b. If all colors are equally likely, how many candies of each color (in a bag of 420 candies) would we expect to see?

c. Is a chi-square test appropriate in this situation? Explain briefly.

d. How many degrees of freedom are there?

A) 2 B) 3 C) 4 D) 5

e. Calculate the chi-square test statistic. Report your answer with three decimal places.

f. Report the p-value for your test. What conclusion can be made about the color distribution for Milk Chocolate M&M's? Use a 5% significance level.

g. Which color contributes the most to the chi-square test statistic? For this color, is the observed count smaller or larger than the expected count?

Answer 1

Are all colors equally likely for Milk Chocolate M&M's? Data collected from a bag of Milk Chocolate M&M's are provided.

Blue            Brown        Green          Orange       Red          Yellow

110                   47               52                 103            58                50

a. State the null and alternative hypotheses for testing if the colors are not all equally likely for Milk Chocolate M&M's.

Ho: colors are all equally likely for Milk Chocolate M&M's.

H1: colors are not all equally likely for Milk Chocolate M&M's.

b. If all colors are equally likely, how many candies of each color (in a bag of 420 candies) would we expect to see?

420/6 = 70

c. Is a chi-square test appropriate in this situation? Explain briefly.

The data are in frequency and the expected value > 5, chi-square test is appropriate.

d. How many degrees of freedom are there?

D) 5

e. Calculate the chi-square test statistic. Report your answer with three decimal places.

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
Blue	110	70.000	40.000	22.857
Brown	47	70.000	-23.000	7.557
Green	52	70.000	-18.000	4.629
Orange	103	70.000	33.000	15.557
Red	58	70.000	-12.000	2.057
Yellow	50	70.000	-20.000	5.714
Total	420	420.000	0.000	58.371
	58.371	chi-square
	5	df
	0.000	p-value

f. Report the p-value for your test. What conclusion can be made about the color distribution for Milk Chocolate M&M's? Use a 5% significance level.

P=0.000 which is < 0.05 level of significance.

Ho is rejected.

We conclude that colors are not all equally likely for Milk Chocolate M&M's.

g. Which color contributes the most to the chi-square test statistic? For this color, is the observed count smaller or larger than the expected count?

Blue color contributes the most to the chi-square test statistic.

For this the observed count larger than the expected count.