Chapter 11.2, Problem 31E

a)

To determine

To verify the conditions for inference.

Answer to Problem 31E

All conditions satisfied.

Explanation of Solution

Given:

		Survey type
		Red	Blue	Control	Total
Color of candy	Red	13	5	8	26
	Blue	7	15	12	34
	Total	20	20	20	60

Calculation:

The conditions of chi square test are: Random, Independence and Large counts.

The volunteers randomly assigned to a survey, so condition of random sample is satisfied.

The sample size is 60 which is less than 10% of all population so, the condition of independent is satisfied.

The expected count of each survey is at least 5 so, condition of large count is satisfied.

b)

To determine

To find p-value using table

Answer to Problem 31E

P-value 0.025 < p < 0.05

Explanation of Solution

Given:

		Survey type
		Red	Blue	Control	Total
Color of candy	Red	13	5	8	26
	Blue	7	15	12	34
	Total	20	20	20	60

The value of chi square test statistic is 6.6516

Formula:

The degrees of freedom = $(r-1)(c-1)$

Calculation:

The degrees of freedom = $(2-1)(3-1)=2$

Using table, p-value is

0.025 < p < 0.05

c)

To determine

To find p-value using calculator

Answer to Problem 31E

P-value is 0.035933

Explanation of Solution

Given:

		Survey type
		Red	Blue	Control	Total
Color of candy	Red	13	5	8	26
	Blue	7	15	12	34
	Total	20	20	20	60

The value of chi square test statistic is 6.6516

Formula:

The degrees of freedom = $(r-1)(c-1)$

Calculation:

The degrees of freedom = $(2-1)(3-1)=2$

Using excel formula, =CHIDIST(6.6516,2)

P-value = 0.035944 = 3.5944%

Therefore, there is 3.5944% chance of obtaining the sample results of more extreme, when the distribution of candy type is truly the same for each survey type.

d)

To determine

To explain conclusion.

Answer to Problem 31E

There is no convincing evidence that the distribution of candy type is not the same for each survey type.

Explanation of Solution

Given:

		Survey type
		Red	Blue	Control	Total
Color of candy	Red	13	5	8	26
	Blue	7	15	12	34
	Total	20	20	20	60

The value of chi square test statistic is 6.6516

P-value = 0.035944

Calculation:

Decision: P-value > 0.01, fail to reject H0.

Conclusion: There is no convincing evidence that the distribution of candy type is not the same for each survey type.