Chapter 11.2, Problem 47E

a)

To determine

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

Answer to Problem 47E

We should use the chi-square test for homogeneity for given setting.

Explanation of Solution

Given:

With many babies being delivered by planned cesarean section, Mrs. McDonald's statistics class hypothesized that there would be fewer younger people born on the weekend. To investigate, they selected a random sample of people born before 1980 and a separate random sample of people born after 1993. In addition to year of birth, they also recorded the day of the week on which each person was born.

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: Year of birth and day of the week. There are two independent samples, people born before 1980 and people born after 1993. Therefore, we should use the chi-square test for homogeneity for given setting.

b)

To determine

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

Answer to Problem 47E

We should use Chi-square test for independence.

Explanation of Solution

Given:

Are younger people more likely to be vegan vegetarian? To investigate, the Pew Research Center asked a random sample of 1430 U.S. adults for their age and whether or not they are vegan vegetarian.

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.

In this scenario, there are two variables. Age and whether they are vegan. There is one random sample of 1430 U.S. adults. Therefore, we should use Chi-square test for independence.