A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. The value of the test statistic and its associated p-value are ________. A) t₁₉₉ = -1.77 and p-value = 0.0385 B) z = -1.77 and p-value = 0.0385 C) t₁₉₉ = -1.77 and p-value = 0.0768 D) z = -1.77 and p-value = 0.0768

Question

Quizplus · Accepted Answer

Since the sample size is large (n=200), we can use a z-test. The test statistic can be calculated as (p_hat - p) / sqrt(p * (1-p) / n), where p_hat is the sample proportion of graduates with a GPA of 3.00 or below, p is the hypothesized proportion (0.20), and n is the sample size. The calculation yields a test statistic of z = -1.77. The p-value can be calculated using a standard normal table or calculator, and is approximately equal to 0.0385. Therefore, the best answer is B.

A University Interested in Tracking Its Honors Program Believes That