"What is procedure for testing the hypothesis about difference between two proportions "

The procedure for testing the hypothesis about the difference between two proportions involves the following steps: 1. *Formulate the null and alternative hypotheses*: - H0: p1 - p2 = 0 (no significant difference between the two proportions) - H1: p1 - p2 ≠ 0 (significant difference between the two proportions) 2. *Choose a significance level*: Select a significance level, usually 0.05 or 0.01. 3. *Calculate the sample proportions*: - p1 = x1 / n1 (proportion of successes in sample 1) - p2 = x2 / n2 (proportion of successes in sample 2) 4. *Calculate the standard error*: - SE = √(p1(1-p1)/n1 + p2(1-p2)/n2) 5. *Calculate the test statistic*: - z = (p1 - p2) / SE 6. *Determine the critical region*: - Compare the calculated z-value to the critical z-value from the standard normal distribution. 7. *Make a decision*: - If the calculated z-value falls in the critical region, reject the null hypothesis (H0) and conclude that there is a significant difference between the two proportions. - If the calculated z-value does not fall in the critical region, fail to reject the null hypothesis (H0) and conclude that there is no significant difference between the two proportions. 8. *Calculate the p-value*: - The p-value is the probability of observing a z-value as extreme or more extreme than the one calculated. - If the p-value is less than the chosen significance level, reject the null hypothesis (H0). Note: This is a two-tailed test, if you want to test for a specific direction of the difference (e.g. p1 > p2), use a one-tailed test.