Question

In an early study, researchers at Ivy University found that 33 percent of the freshmen had received at least one A in their first semester. Administrators are concerned that grade inflation has caused this percentage to increase. In a more recent study, of a random sample of 500 freshmen, 185 had at least one A in their first semester. Test the claim at α = .05.

0.0327; the percentage has risen

   

0.9736; the percentage has not changed

   

0.0654; the percentage has not changed

   

0.0327; the percentage has not changed

   

0.9736; the percentage has risen

PLEASE EXPLAIN. I dont need the answer just reviewing for a quiz.

Answer 1

Here we have x -185, n-500, p=--0.37 п Hypotheses are Но: р3D0.33 H:p>0.33 Level of significance: a 0.05 Test is right tailed. The standard deviation is: P(1-р) -sqrt((0.33*(1-0.33))/500) п = 0.021 Test Statistics: р-р - (0.37-0.33)/(0.021) Z = = 1.9 Critical value: CV 1.645 Rejection Region: If z > 1.645, Reject HO Decision: Since test statistics lies in rejection region so we reject the null hypothesis P-value: P-value-0.0287 Decision: Since p-value is less than level of significance so we reject the null hypothesis =NORMSINV(1-0.05) -1-NORMSDIST(1.9) Excel function for critical value: Excel function for p-value:

Conclusion; There is evidence to conclude that the percentage has risen.