Question

Joan Nguyen recently claimed that the proportion of college-aged males with at least one pierced ear is as high as the proportion of college-aged females. She conducted a survey in her classes. Out of 106 males, 19 had at least one pierced ear. Out of 84 females, 47 had at least one pierced ear. Do you believe that the proportion of males with at least one pierced ear is different from the proportion of females with at least one pierced ear?

State the distribution to use for the test. (Round your answers to four decimal places.)

P'_m − P'~ ( , ) ?

Answer 1

Answer:

Given,

x1 = 19 , x2 = 47

sample n1 = 106 , n2 = 84

sample p1 = x1/n2 = 19/106 = 0.1792

p2 = x2/n2 = 47/84 = 0.5595

Standard error = sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)

substitute values

= sqrt(0.1792(1-0.1792)/106 + 0.5595(1-0.5595)/84)

= 0.0657

consider,

test statistic z = (p1 - p2)/se

substitute values

= (0.1792 - 0.5595)/0.0657

z = -5.785

P value = 0

Here we observe that, p value < 0.05, so we reject Ho, we have enough evidence.