Chapter 11.2, Problem 35E

To determine

To perform chi square test of independence.

Answer to Problem 35E

There is no convincing evidence that the distributions of color differ for name-brand gummy bears and store-brand gummy bears.

Explanation of Solution

Given:

	Name	Store	Total
Red	137	212	349
Green	53	104	157
Yellow	50	85	135
Orange	81	127	208
White	52	94	146
Total	373	622	995

Calculation:

Null and alternative hypotheses:

  $H_0$ : The distribution of color is same for each brand type.

  $H_a$ : The distribution of color is not same for each brand type.

Using excel formula,

		Name	Store	Total
Red	Observed	137	212	349
	Expected	130.83	218.17	349.00
	(O - E)² / E	0.29	0.17	0.47
Green	Observed	53	104	157
	Expected	58.86	98.14	157.00
	(O - E)² / E	0.58	0.35	0.93
Yellow	Observed	50	85	135
	Expected	50.61	84.39	135.00
	(O - E)² / E	0.01	0.00	0.01
Orange	Observed	81	127	208
	Expected	77.97	130.03	208.00
	(O - E)² / E	0.12	0.07	0.19
White	Observed	52	94	146
	Expected	54.73	91.27	146.00
	(O - E)² / E	0.14	0.08	0.22
Total	Observed	373	622	995
	Expected	373.00	622.00	995.00
	(O - E)² / E	1.13	0.68	1.81
		1.81	chi-square
		4	df
		.7698	p-value

Decision: P-value = 0.7698 > 0.05, fail to reject.

Conclusion: There is no convincing evidence that the distributions of color differ for name-brand gummy bears and store-brand gummy bears.