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Scenario Three: A group of parents believes that the proportion of students who find their college...

Scenario Three: A group of parents believes that the proportion of students who find their college experience extremely rewarding does not equal 50%. They decide to test this hypothesis using a significance level of .05. They conduct a random sample of 100 students and 34 say they find their college experience extremely rewarding. You only need to redo the steps below to receive full credit for scenario three.

Based on the type of test this is (right, left, or two-tailed); determine the following for this problem.

4. Critical Value(s): _______________________

5. P-value Table A.3 _______________________ P-value Calculator:________________

P-value Table A.2 _______________

6: Can you reject? _______________________

7. Conclusion: Can we conclude or can we not conclude that the proportion of students who find their college experience extremely rewarding does not equal 50%?

Continue with Scenario Three with a significance level of .001. The test condition is still “does not equal 50%.”

8.a Critical Values for two-tailed test with α = .001: _____________________

8.b Conclusion: Can we conclude with a significance level of .001 that the proportion of students who find their college experience extremely rewarding does not equal 50%?

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Answer #1

Data:    

n = 100   

p = 0.5   

p' = 0.34   

Hypotheses:    

Ho: p = 0.5   

Ha: p ≠ 0.5   

Decision Rule:    

α = 0.05   

Lower Critical z- score = -1.9600   

Upper Critical z- score = 1.9600   

Reject Ho if |z| > 1.9600   

Test Statistic:    

SE = √{p (1 - p)/n} = √(0.5 * (1 - 0.5)/100) = 0.0500

z = (p'- p)/SE = (0.34 - 0.5)/0.05 = -3.2000

p- value = 0.0014   

Decision (in terms of the hypotheses):    

Since 3.2000 > 1.9600 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is sufficient evidence that the proportion is not 50%

ANSWERS:

4. Critical Value(s): = ± 1.96

5. P-value = 0.0014

6: Can you reject? Yes

7. Conclusion: We can conclude that the proportion of students who find their college experience extremely rewarding does not equal 50%

8.a Critical Values for two-tailed test with α = .001: = ± 3.2905

8.b Conclusion: We can't conclude with a significance level of .001 that the proportion of students who find their college experience extremely rewarding does not equal 50%.

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