Question

Find the weighted estimate, p to test the claim that p₁ > p₂. Use a "alpha" = 0.01. The sample statistics listed below are from independent samples.

Sample statistics: n₁ = 100, x₁ = 38, n₂ = 140, x₂ = 50.

A) 0.367

B) 0.179

C) 0.523

D) 0.633

Answer 1

The correct weighted estimate, p, needed to test the claim that p₁ > p₂ with a significance level of 0.01 using the given sample statistics is option A (0.367).

Step-by-step explanation:

The student is asking for the weighted estimate, p, to test the hypothesis that the proportion p₁ is greater than p₂ using given sample statistics. The significance level (α) for the test is 0.01. To find the weighted estimate, firstly, we calculate the sample proportions π₁ = x₁/n₁ = 38/100 and π₂ = x₂/n₂ = 50/140. Then, we find the weighted proportion using the formula: π_w = (x₁ + x₂) / (n₁ + n₂). By substituting the given values, we get π_w = (38 + 50) / (100 + 140) = 88/240.

Upon calculation, π_w = 0.3667, which rounds to approximately 0.367. This result corresponds to option A. So, option A (0.367) is the correct weighted estimate, p, for testing the hypothesis that p₁ is greater than p₂ at the 0.01 significance level.