A study done on a marriage counseling course showed that the proportion of couples for which the communication program can prevent divorce is 78

%

. Suppose we have strong reason to believe the proportion is less than 78

%

, 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.



H

0

: 



H

1

: 

In hypothesis testing regarding the effectiveness of the marriage counseling program, we define the null and alternative hypotheses as follows:

- **Null Hypothesis (H0)**: The proportion of couples for which the communication program can prevent divorce is equal to 78%.  
  \( H_0: p = 0.78 \)

- **Alternative Hypothesis (H1)**: The proportion of couples for which the communication program can prevent divorce is less than 78%.  
  \( H_1: p < 0.78 \)

This setup allows you to test if there is sufficient evidence to support the claim that the program's effectiveness is lower than previously thought. 

Would you like more details on how to conduct the hypothesis test or any other related concepts? Here are some related questions you might consider:

1. What statistical test would be appropriate for this hypothesis test?
2. How do you calculate the test statistic for this hypothesis?
3. What is the significance level, and how does it affect the test?
4. How would you interpret the results if you reject the null hypothesis?
5. What assumptions need to be checked before performing this test?

**Tip**: Always ensure your sample size is adequate to achieve reliable results when conducting hypothesis tests.

A study done on a marriage counseling course showed that the proportion of couples for which the communication program can prevent divorce is 78%. Suppose we have strong reason to believe the proportion is less than 78%, and we carry out a hypothesis test. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.

Explore the hypothesis testing framework for a marriage counseling program, where the null hypothesis states that 78% of couples can avoid divorce, and the alternative hypothesis suggests it is less. Understand the statistical significance and implications of the results.

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