Question

In: Statistics and Probability

To investigate whether it helps to have a "white-sounding" first name when looking for a job,...

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-soundingpblack-sounding. Round your test statistic to two decimal places and your P-value to four decimal places.)

z=

p-value=

Solutions

Expert Solution

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


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