In: Statistics and Probability
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 169 responses. (Use pwhite-sounding − pblack-sounding. Round your test statistic to two decimal places and your P-value to four decimal places.)
z=
p-value=
Solution :
Given that,
n1 = 5000
x1 = 2500
Point estimate = sample proportion = 1 = x1 / n1 = 0.5
n2 = 256
x2 = 169
Point estimate = sample proportion = 2 = x2 / n2 = 0.660
The value of the pooled proportion is computed as,
= ( x1 + x2 ) / ( n1 + n2 )
= ( 2500 + 169) / ( 5000 + 256)
= 0.508
1 - = 0.492
This a two-tailed test.
The null and alternative hypothesis is,
Ho: p1 = p2
Ha: p1 p2
Test statistics
z = (1 - 2 ) / *(1-) ( 1/n1 + 1/n2 )
= ( 0.5 - 0.660) / ( 0.508 * 0.492) ( 1/5000 + 1/256)
= -5.00
P-value = 2 * P(Z < z )
= 2 * P(Z < -5.00 )
= 2 * 0.0000
= 0.0000