Pager (2003) reported that white men with a felony record were as likely to receive a...

Pager (2003) reported that white men with a felony record were as likely to receive a job interview than were black men without a felony record. Using the data below, replicate her findings. Specifically, among 149 black respondents without a felony record, the probability that a potential employer called them for a job interview was .14. Among 53 white respondents with a felony record, the probability that a potential employer called them for a job interview was .17.

A) What is the 95% confidence interval for the probability that black men without a felony were called back for a job interview?

B)Suppose Pager’s research hypothesis was that a criminal record was more important than race in determining the likelihood of employment. Thus, she expected that black men without felonies (BM) were more likely to be interviewed than white men with felonies (WMF). Test the Null Hypothesis of no difference in the likelihoods. State the Null and Research Hypotheses

C)Using a .01 alpha level, determine the critical value of the test.

D)Calculate the obtained value for your test.

E) Interpret the test results.

Solutions

Expert Solution

Sample proportion of black respondents without a felony record called for interview, p = 0.14

Standard error of sample proprotion, SE = = 0.0284

Z value for 95% confidence interval is 1.96

95% confidence interval for the probability that black men without a felony were called back for a job interview is,

(0.14 - 1.96 * 0.0284 , 0.14 + 1.96 * 0.0284)

(0.0843 , 0.1957)

Null Hypothesis H0: Proportion of black men without felonies (BM) to be interviewed is equal to the proportion of white men with felonies (WMF).

Alternative Hypothesis Ha: Proportion of black men without felonies (BM) to be interviewed is greater than he proportion of white men with felonies (WMF).

For .01 alpha level, the critical value of the z test statistic is 2.326

Pooled proportion, p = (0.14 * 149 + 0.17 * 53) / (149 + 53) = 0.1479

Standard error of difference in proportions, SE =

= 0.0567772

Test statistic, z = (0.14 - 0.17)/0.0567772 = -0.53

Since the test statistic is less that the critical value, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that the proportion of black men without felonies (BM) to be interviewed is greater than the proportion of white men with felonies (WMF).

orchestra answered 1 year ago

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