Exhibit 9-5.A university interested in tracking their 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. Refer to Exhibit 9-5.At a 5% significance level,the decision is to ___________. A)Reject H₀;we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20. B)Reject H₀;we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20. C)Do not reject H₀;we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20. D)Do not reject H₀;we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20.

Question

Quizplus · Accepted Answer

The sample proportion of graduates with a GPA of 3.00 or below is 30/200 = 0.15. The null hypothesis is that the population proportion is 0.20, and the alternative hypothesis is that the population proportion is less than 0.20. The test statistic is z = (0.15 - 0.20) / sqrt(0.20 * 0.80 / 200) = -2.24. The p-value is P(Z < -2.24) = 0.012. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20.