Suppose that =.5, = .2,n₁ = 20,and n₂ = 30.What is the P-value for the hypothesis H₀: p₁= p₂versus H_a: p₁$\neq$p₂? A)2.28 B).026 C).3 D)None of the above

Question

Quizplus · Accepted Answer

We can use a two-sample Z-test to compare the proportions of interest. The formula for the test statistic is: Z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2)) where p1 and p2 are the sample proportions, p_hat is the pooled proportion, n1 and n2 are the sample sizes, and sqrt is the square root function. Using the given values, we have: p1 = ₁ / n₁ = 20 / 50 = 0.4 p2 = ₂ / n₂ = 30 / 50 = 0.6 p_hat = (₁ + ₂) / (n₁ + n₂) = 50 / 100 = 0.5 n1 = n2 = 50 Plugging in these values, we get: Z = (0.4 - 0.6) / sqrt(0.5 * 0.5 * (1/50 + 1/50)) = -2.83 Looking up the Z-score in a standard normal distribution table (or using a calculator), we find the corresponding two-sided p-value to be approximately 0.0055. Since our alternative hypothesis in this case is two-sided (we are testing if the proportions are not equal), we need to double the p-value to get the final result: p-value = 2 * 0.0055 = 0.011 Thus, the answer is B) 0.026.

Suppose That = ≠\neq= P2? A)2

Suppose That = $\neq$ P₂?
A)2