Chapter 11.2, Problem 49E

a)

To determine

To determine which chi-square test is appropriate for given setting.

Answer to Problem 49E

We should use Chi-square test for independence.

Explanation of Solution

Given:

		Gender
		Female	Male
Living location	Parent's home	923	986
	Another person's home	144	132
	Own place	1294	1129
	Group quarters	127	119

First, we need to know which test should be apply for a specific scenario. There are three tests:

Chi-square goodness-of-fit test, chi-square test for homogeneity, chi-square test for independence.

We will know in details about these all tests.

When we are interested in the distribution of one variable, then we will use a chi-square goodness-of-fit test. When we are interested in the distribution of two variables in which there are multiple independent samples, then in this scenario we have to use a chi-square test for homogeneity. When we are interested in the distribution of two variables and if there is a single sample, then we would like to use a chi-square test for independence.

For given setting, we are given in two variables: Gender and living location There is one random sample. Therefore, we should use Chi-square test for independence.

b)

To determine

To state the null and alternative hypotheses.

Answer to Problem 49E

  $H_0$ : There is no association between gender and living location.

  $H_a$ : There is association betweengender and living location.

Explanation of Solution

Given:

		Gender
		Female	Male
Living location	Parent's home	923	986
	Another person's home	144	132
	Own place	1294	1129
	Group quarters	127	119

Calculation:

The null and alternative hypotheses:

  $H_0$ : There is no association between gender and living location

  $H_a$ : There is association between gender and living location

c)

To determine

To verify the conditions for inference.

Answer to Problem 49E

All conditions satisfied.

Explanation of Solution

Given:

Calculation:

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

The sample is randomly selected, so condition of random sample is satisfied.

The sample size 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.

d)

To determine

To explain conclusion.

Answer to Problem 49E

There is convincing evidence that the association between gender and living location.

Explanation of Solution

Given:

Calculation:

The p-value = 0.012. Therefore, if there is no association between the two variables, then the probability of getting a similar or more extreme sample as the given sample is 0.012 or 1.2%.

Decision: P-value < 0.05, reject H0.

Conclusion: There is convincing evidence that the association between gender and living location.