Question

To investigate whether it helps to have a "white-sounding" first name when looking for a job, the researchers sent 5000 resumes in response to ads that appeared in magazines. The resumes were identical except that 2500 of them had "white-sounding" first names, such as Brett and Emily, whereas the other 2500 had "black-sounding" names such as Tamika and Rasheed. Resumes of the first type elicited 256 responses and resumes of the second type only 163 responses. (Use pwhite-sounding − pblack-sounding. Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P	=

Answer 1

p1cap = X1/N1 = 256/2500 = 0.1024
p1cap = X2/N2 = 163/2500 = 0.0652
pcap = (X1 + X2)/(N1 + N2) = (256+163)/(2500+2500) = 0.0838

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.1024-0.0652)/sqrt(0.0838*(1-0.0838)*(1/2500 + 1/2500))
z = 4.75

P-value Approach
P-value = 0 .0000
As P-value < 0.05, reject the null hypothesis.