Question

Which test? Determine which chi-square test is appropriate in each of the following settings. Explain your reasoning.

a. 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.

b. Are younger people more likely to be vegan/vegetarian? To investigate, the Pew Research Center asked a random sample of $1480$ U.S. adults for their age and whether or not they are vegan/vegetarian.

Short answer

a) A chi-square test for homogeneity is used when we are interested in the distribution of two variables and there are several independent samples.

b) A chi-square test for independence is used when we are interested in the distribution of two variables and there is only one sample.

Step-by-step solution

Part (a) Step 1: Given information 

We have to tell about statistics class hypothesized that there would be fewer younger people born on the weekend. To investigate.

Part (a) Step 2: Explanation

A chi-square goodness-of-fit test will be used if we are only interested in the distribution of one variable.

A chi-square test for homogeneity is used when we are interested in the distribution of two variables and there are several independent samples.

A chi-square test for independence is used when we are interested in the distribution of two variables and there is only one sample.

Two variables are of interest: the year of birth and the day of the week. We should also notice that we have two independent samples, so the chi-square test for homogeneity should be used.

Part (b) Step 1: Given information 

We have to tell about are younger people more likely to be vegan/vegetarian.

Part (b) Step 2: Explanation

• A chi-square goodness-of-fit test will be used if we are only interested in the distribution of one variable.
• A chi-square test for homogeneity is used when we are interested in the distribution of two variables and there are several independent samples.
• A chi-square test for independence is used when we are interested in the distribution of two variables and there is only one sample.
• We're looking for two things: age and whether or not they're vegan or vegetarian. We should also keep in mind that we only have one random sample, thus we should apply the chi-square test to determine independence.