Consider performing a hypothesis test to determine if Republicans, Democrats, and Independents feel differently about the strictness of current gun laws in America.

The null hypothesis is that There is no relationship between political party and opinion on gun law strictness.

The alternate hypothesis is that There is a relationship between political party and opinion on gun law strictness.

Question

Consider performing a hypothesis test to determine if Republicans, Democrats, and Independents feel differently about the strictness of current gun laws in America.

The null hypothesis is that There is no relationship between political party and opinion on gun law strictness.

The alternate hypothesis is that There is a relationship between political party and opinion on gun law strictness.

BlackTom AI · Accepted Answer

To analyze this question, I will restate the provided items and then evaluate each option one by one.
Question restatement: You are performing a hypothesis test to determine whether Republicans, Democrats, and Independents feel differently about the strictness of current gun laws in America. The null hypothesis is that there is no relationship between political party and opinion on gun law strictness. The alternative hypothesis is that there is a relationship between political party and opinion on gun law strictness.
Option 1: 'There is no relationship between political party and opinion on gun law strictness.'
- This option matches the standard form of the null hypothesis for a test of independence or association between two categorical variables (political party and opinion on gun law strictness). It asserts no relationship or association between the categories.
- In the context of a chi-square test of independence (or similar), this would be the hypothesis you test against.
- This option is correct as the null hypothesis because it correctly states no relationship as the default assumption to be tested.

Option 2: 'There is a relationship between political party and opinion on gun law strictness.'
- This option represents the alternative hypothesis, which posits that there is some association or relationship between the two categorical variables.
- In hypothesis testing, the alternative is what you would conclude if you reject the null; it is not the null itself.
- This option is correct as the alternative hypothesis because it correctly states that a relationship exists, but it is the counterpart to the null.

Additional notes to avoid confusion:
- The two statements are complementary: one expresses no relationship (null), the other expresses a relationship (alternative).
- In practice, the researcher would collect data on party affiliation and opinions, compute a test statistic (e.g., chi-square), and decide whether to reject the null in favor of the alternative based on a chosen significance level.
- Since there were no other answer options provided, there are no additional distractors to evaluate here; the two options correspond precisely to the standard pair of hypotheses in a test of independence.

Su25-STATS-141-01/BIO-141-01 Homework 5: Differences in Proportions & Chi-Square Test of Independence

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