Question

Suppose as a part of a national study of economic competitiveness a marketing research firm randomly sampled 200 adults between the ages of 27 and 35 living in City A and 140 adults between the ages of 27 and 35 living in City B. Each adult selected in the sample was asked, among other things, whether they had a college degree. From the City A sample 76 adults answered yes and from the City B sample 39 adults answered yes when asked if they had a college degree. Based on the sample data, can we conclude that there is a difference between the population proportions of adults between the ages of 27 and 35 in the two cities with college degrees? Use a level of significance of 0.05 to conduct the appropriate hypothesis test. If you were testing the hypothesis described above, calculate the value of the z-test statistic you would use.

Answer 1

The solution to this problem is given by

Solution briver data is City City B n- ng= 140 Samble Size Nomber of 76 Xo = 39 39 76 goo ng ni Succes Proportion of i=x Pea Success 0.38 Pooled Proportions = P = Xit Xe = 76+39 = 0.338 0.2786 co , 12 htha Qoot 140 E1-0.338 0.662 Test Statistics o be 0.38 -0.2786 2= pofth the (0.338)(0.662) 1 + goo 140 2 - 1.9453 Test Statistics Statistics = Z - 1.9453