Question

Assume that you plan to use a significance level of a = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the p-value for the hypothesis test. n1 = 50, n2 = 75, x1 = 20, x2 = 15?

Answer 1

To test the claim that two proportions are equal, calculate the pooled proportion, standard error, test statistic (Z-score), and find the corresponding p-value. If the p-value is less than the significance level (0.05), the null hypothesis is rejected, indicating a difference between the proportions.

Step-by-step explanation:

To find the p-value for the hypothesis test comparing two proportions (p1 and p2), given sample sizes of n1 = 50 and n2 = 75, and numbers of successes x1 = 20 and x2 = 15, we can use a Z-test for two proportions.

The test statistic for two proportions can be calculated with the following steps:

1. Calculate the pooled proportion (p) using the formula: p = (x1 + x2) / (n1 + n2).
2. Calculate the standard error (SE) for the difference in proportions with the formula: SE = sqrt[p * (1 - p) * ((1/n1) + (1/n2))].
3. Calculate the Z-score (test statistic) with the formula: Z = (p1 - p2) / SE, where p1 = x1/n1 and p2 = x2/n2.
4. Use a standard normal distribution table or technology to find the p-value corresponding to the calculated Z-score.

The null hypothesis is that there is no difference between the two proportions (p1 = p2). After calculating the test statistic, we compare the p-value to the significance level (alpha = 0.05). If the p-value is less than alpha, we reject the null hypothesis, indicating that there is evidence of a difference between the two proportions.