An article claimed that \"those with a college degree reported a higher incidenc

Question

An article claimed that "those with a college degree reported a higher incidence of sunburn than those without a high school degree—41 percent versus 24 percent." For purposes of this exercise, suppose that these percentages were based on random samples of size 200 from each of the two groups of interest (college graduates and those without a high school degree). (Use a statistical computer package to calculate the P-value. Use pcollege graduates pwithout a high school degree. Round your test statistic to two decimal places and your P-value to four decimal places.)

Is there convincing evidence that the proportion who experience a sunburn is higher for college graduates than it is for those without a high school degree? Answer based on a test with a 0.05 significance level.

Explanation / Answer

Data:    

n1 = 200   

n2 = 200   

p1 = 0.41   

p2 = 0.24   

Hypotheses:    

Ho: p1 p2    

Ha: p1 > p2    

Decision Rule:    

= 0.05   

Critical z- score = 1.644853627   

Reject Ho if z > 1.644853627   

Test Statistic:    

Average proportion, p = (n1p1 + n2p2)/(n1 + n2) = (200 * 0.41 + 200 * 0.24)/(200 + 200) = 0.325

q = 1 - p = 1 - 0.325 = 0.675

SE = [pq * {(1/n1) + (1/n2)}] = (0.325 * 0.675 * ((1/200) + (1/200))) = 0.046837485

z = (p1 - p2)/SE = (0.41 - 0.24)/0.046837484987988 = 3.629571486

p- value = 0.000141946   

Decision (in terms of the hypotheses):    

Since 3.629571486 > 1.644853627 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

It appears that p1 > p2   

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