Question

Assume that you plan to use a significance level of μ = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the p-value. Also, state the statistical conclusion. Round your answer to the nearest thousandth. n1 = 100, N₂ = 100, x1 = 42, x2 = 45.

Answer 1

To find the p-value, perform a two-proportion z-test. Calculate the test statistic using the formula: z = (p1 - p2) / sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)). The p-value is approximately 0.406.

Step-by-step explanation:

To find the p-value, we need to perform a two-proportion z-test. Let's define p1 as the proportion of successes in population 1 and p2 as the proportion of successes in population 2.

To calculate the test statistic, we use the formula: z = (p1 - p2) / sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2)).

Plugging in the values, we get: z = (0.42 - 0.45) / sqrt((0.42(1-0.42)/100) + (0.45(1-0.45)/100)).

Calculating the test statistic, z ≈ -0.238.

The p-value can be calculated using a z-table or a calculator. In this case, the p-value is approximately 0.406.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to support the claim that p1 is equal to p2.