Chapter 11.2, Problem 48E

a)

To determine

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

Answer to Problem 48E

We should use Chi-square test for independence.

Explanation of Solution

Given:

Does chocolate help heart-attack victims live longer? Researchers in Sweden randomly selected 1169 people who had suffered heart attacks and asked them about their consumption of chocolate in the previous year. Then the researchers followed these people and recorded whether or not they had died within 8 years

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: Chocolate consumption and death with 8 years. There is one random sample of 1169 people who had suffered heart attacks. Therefore, we should use Chi-square test for independence.

b)

To determine

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

Answer to Problem 48E

We should use Chi-square test for homogeneity.

Explanation of Solution

Given:

Random-digit-dialing telephone surveys used to exclude cell-phone numbers. If the opinions of people who have only cell phones differ from those of people who have landline service, the poll results may not represent the entire adult population. The Pew Research Center interviewed separate random samples of cell-only and landline telephone users who were less than 30 years old and asked them to describe their political party affiliation.

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. Type of telephone and political party. There are two random samples of cell-only and landline telephone users. Therefore, we should use Chi-square test for homogeneity.