https://file.aiquickdraw.com/mathbot/file/1727665508221n6rfn2w8.jpg

The problem asks to set up the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) for a hypothesis test regarding the proportion of couples for which a communication program prevents divorce. The given information states that the proportion is 76%, but we are testing if the proportion is **less than** 76%.

### Null Hypothesis (\( H_0 \)):
The null hypothesis typically states that there is **no change or difference** from the known proportion, meaning:
\[
H_0: p = 0.76
\]
where \( p \) is the proportion of couples whose divorce is prevented by the program.

### Alternative Hypothesis (\( H_1 \)):
Since we want to test if the proportion is **less than** 76%, the alternative hypothesis is:
\[
H_1: p < 0.76
\]

So, the null and alternative hypotheses are:
- \( H_0: p = 0.76 \)
- \( H_1: p < 0.76 \)

Let me know if you need any further clarifications, or I can check your answers.

Here are 5 relative questions for further exploration:
1. What is the significance level commonly used in hypothesis tests?
2. How do you calculate the test statistic for a proportion hypothesis test?
3. What does it mean if the null hypothesis is rejected?
4. How can we interpret a p-value in a hypothesis test?
5. What role does sample size play in determining the power of a test?

**Tip:** In hypothesis testing, always ensure that the alternative hypothesis aligns with the direction of the test (greater than, less than, or not equal to).

A study done on a marriage counselling course showed that the proportion of couples for which the communication program can prevent divorce is 76%. Suppose we have strong reason to believe the proportion is less than 76%, and we carry out a hypothesis test. State the null hypothesis H_0 and the alternative hypothesis H_1 that we would use for this test.

Learn how to set up null and alternative hypotheses for a proportion test, based on a study about a communication program preventing divorce. The problem involves hypothesis testing, focusing on the proportion of couples and testing if it is less than 76%.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation