Question

7. Test H₀: π = 0.25 versus H_A: π ¹ 0.25 with p = 0.33 and n = 100 at alpha = 0.05 and 0.10.

8. Test at α =.05 and 0.10 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 500 students, 265 favor the system?

Answer 1

Question 7:

As we are testing here whether the proportion is greater than 0.25, therefore the test statistic here is computed as:

As this is a one tailed test, the p-value here is computed from the standard normal tables as:

p = P(Z > 1.8475) = 0.0323

As the computed p-value here is 0.0323 < 0.1 and 0.0323 < 0.05, therefore the test is significant for both level of significance 0.05 and 0.1. Therefore we can reject the null hypothesis here and conclude that we have sufficient evidence that the proportion here is more than 0.25.