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? (Use

α = 0.05.)

• What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

• Part (f)

  What is the p-value?

Answer 1

Total number of sample 1 (n1) = 106

Total number of sample 2 (n2) = 84

number of favourable events (X1) = 19

number of favourable events (X2) = 47

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = 2(2.2834234790448042e-08)

P = 0.0

Since, the test is two-tail test at \alpha = 0.05

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.96or greater than the critical value 1.96

The statistic value, -5.47 is less than the critical value -1.96. Hence, reject the null hypothesis.