Question

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken 5 years age. Five years age, a sample of 270 students showed that 120 considered themselves overweight. This year a poll of 300 students showed that 140 considered themselves overweight. At a 5% level of significance, test to see if there is any difference in the proportion of college students who consider themselves overweight between the two polls. What is your conclusion?

Answer 1

Data:    

n1 = 270   

n2 = 300   

p1 = 0.444444444   

p2 = 0.466666667   

Hypotheses:    

Ho: p1 = p2    

Ha: p1 ≠ p2    

Decision Rule:    

α = 0.05   

Lower Critical z- score =   -1.959963985

Upper Critical z- score = 1.959963985

Reject Ho if |z| >   1.959963985

Test Statistic:    

Average proportion, p = (n1p1 + n2p2)/(n1 + n2) = (270 * 0.444444444444444 + 300 * 0.466666666666667)/(270 + 300) = 0.456140351

q = 1 - p = 1 - 0.456140350877193 = 0.543859649

SE = √[pq * {(1/n1) + (1/n2)}] = √(0.456140350877193 * 0.543859649122807 * ((1/270) + (1/300))) = 0.041781842

z = (p1 - p2)/SE = (0.444444444444444 - 0.466666666666667)/0.0417818421149385 = -0.531863151

p- value = 0.59482078   

Decision (in terms of the hypotheses):    

Since 0.531863151 < 1.959963985 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence of a significant difference between the proportions.

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