The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one observed under the null hypothesis. For a one-tailed z-test, we calculate the p-value based on the cumulative distribution function (CDF) of the standard normal distribution.

Given that we have a positive z-value, the p-value is:

$\text{p-value} = 1 - \Phi(z)$

Where $\Phi(z)$ is the cumulative probability up to the z-value.

Let's calculate the p-value.from scipy.stats import norm

Calculate the p-value for the one-tailed test

p_value = 1 - norm.cdf(z) p_valueThe p-value is approximately $0.00695$.

Conclusion:

Since the p-value ($0.00695$) is much smaller than the significance level ($\alpha = 0.10$), we have strong evidence to reject the null hypothesis. This further supports the marriage counselor's claim that her program can prevent divorce in more than 75% of married couples.

Would you like further details or explanations?

Related Questions

1. How is the p-value interpreted in hypothesis testing?
2. What is the relationship between the p-value and the significance level?
3. How does the p-value change with different sample sizes?
4. Why is the p-value different for one-tailed vs. two-tailed tests?
5. What are Type I and Type II errors in hypothesis testing?
6. How would the results differ with a significance level of 0.05?
7. What is the difference between statistical significance and practical significance?
8. How do confidence intervals relate to hypothesis testing?

Tip: Always compare the p-value with the chosen significance level ($\alpha$) to make a decision on the hypothesis test.