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 = 0.0384 B) z = -1.77 and p-value = 0.0384 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 null hypothesis is that the proportion of graduates with a GPA of 3.00 or below is 0.20, and the alternative hypothesis is that the proportion is less than 0.20.

The calculated z-score is:
z=(0.15-0.20)/sqrt(0.20*0.80/200) = -1.77

The associated p-value can be found using a standard normal table or calculator:
p-value = P(Z < -1.77) = 0.0384

Therefore, the correct answer is B: z = -1.77 and p-value = 0.0384.

A University Interested in Tracking Its Honors Program Believes That