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—46 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.)

Explanation / Answer

Null Hypothesis : people with a college degree have a same degree of incidence of sunburn than those without a high school degree. pcollegegraduates = pwithouta high school degree

Alternative Hypothesis : people with a college degree reported a higher incidence of sunburn than those without a high school degree. pcollege graduates > pwithout a high school degree

By survey results:

p1 = 0.46 and p2 = 0.24

n1 = n2 = 200

so pooled estimate p* = ( n1p1 + n2p2)/(n1 + n2) = ( 92 + 48) / ( 200 + 200) = 0.35

Standard error of estimate SE0 = sqrt [ p* ( 1- p* ) (1//n1 + 1/n2 )] = sqrt [ 0.35 * 0.65 *1/100] = 0.0477

Test Statistic :

Z = (p1 - p2 ) / SE0 = ( 0.46 - 0.24)/ 0.0477 = 4.61

p - value = 0.0001 for the above given Z - value

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