Question

A political action committee believes that peoples' income and their opinions about same sex marriage are not independent. They conduct a survey to gather data for a hypothesis test to test their belief. Participants are asked to choose their income bracket from a list of several possibilities. They are also asked to indicate whether they support, oppose, or are neutral toward same sex marriage. Which of the following is the most appropriate pair of hypotheses to use for this test? Group of answer choices

Answer 1

Null hypothesis
`(\(H_0\))`: People's income and opinions on same-sex marriage are independent. Alternative hypothesis
`(\(H_a\))`: People's income and opinions on same-sex marriage are not independent. This is for a chi-square test for independence.

To determine the most appropriate pair of hypotheses for testing the belief that people's income and their opinions about same-sex marriage are not independent, you would typically use a chi-square test for independence. The null hypothesis
`(\(H_0\))` for this test typically assumes independence, while the alternative hypothesis
`(\(H_a\)` or
`\(H_1\))` suggests dependence.

The null hypothesis
`(\(H_0\))`: There is no significant association between people's income and their opinions about same-sex marriage.

The alternative hypothesis
`(\(H_a\)` or \
`(H_1\))\\`There is a significant association between people's income and their opinions about same-sex marriage.

In symbolic notation:

`\(H_0\): \( \text{Income and opinion about same-sex marriage are independent} \)`

`\(H_a\): \( \text{Income and opinion about same-sex marriage are not independent} \)`

This set of hypotheses is appropriate for a chi-square test for independence, where the test would assess whether there is a statistically significant relationship between income and opinions about same-sex marriage.