Question

In: Statistics and Probability

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.

Expert Solution

A)

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)

B)

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).

C)

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

D)

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

E)

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

In 2003, it was reported that 40% of all car accidents in Connecticut were alcohol related....

In 2003, it was reported that 40% of all car accidents in Connecticut were alcohol related. Suppose we take a random sample of 100 car accidents in Connecticut and let X be the number that are alcohol related. Find the probability that at least 40 were alcohol related and at least 40 were not alcohol related.

It has been reported that men are more likely than women to participate in online auctions.

It has been reported that men are more likely than women to participate in online auctions. A recent study found that 52% of Internet shoppers are women and that 35% of Internet shoppers have participating in online auctions. Moreover, 25% of online shoppers were men and had participated in online auctions.a) Construct the contingency table below. b) Given that an individual participates in online auctions, what is the probability that individual is a man? c) Given that an individual participates in online...

1. Historically, women were less likely to invest in a college degree than men. Why was...

1. Historically, women were less likely to invest in a college degree than men. Why was this the case? What has changed to reverse this trend? 2. Explain the economics underlying the human capital investment decision (specifically, the decision to go to college versus sticking with just the high school diploma). 3. Empirical evidence shows clearly that, on average, individuals with more years of education earn more money, other things equal. Two different theories support this evidence: human capital theory...

women who reported an earlier age at menarche were more likely to be heavier at age...

women who reported an earlier age at menarche were more likely to be heavier at age 7 years (average weight = 24.7 kg) compared with those who reported a later age at menarche (average weight = 23.2 kg) (P = 0.01). The correlation between weight at age 7 years and age at menarche was -0.17 (P = 0.009). Q: The -0.17 value is for what? how to find it and why it is important to mention?

In 1995 , one county reported that among 3193 white women who had babies, 148 were...

In 1995 , one county reported that among 3193 white women who had babies, 148 were multiple births. There were also 29 multiple births to 648 black women. Does this indicate any racial difference in the likelihood of multiple births? a) Test an appropriate hypothesis and state your conclusion. b) If your conclusion is incorrect, which type of error did you commit?

In 2003, CNN reported that “researchers found that classical music […] was the most successful in...

In 2003, CNN reported that “researchers found that classical music […] was the most successful in encouraging people to part with their cash [in restaurants], with diners spending more than u$s 40 a head.” “With no background music, spending [in meals] fell to around u$s 35).” a. Graphically show the market for restaurant food when no restaurant plays any music. Make sure you include demand and supply curves, and show the equilibrium price and quantity. b. Now suppose that all...

Passwords, red heads, and a z test: The BBC reported that red-haired women were more likely...

Passwords, red heads, and a z test: The BBC reported that red-haired women were more likely than others to choose strong passwords (Ward, 2013). How might a researcher study this? Computer scientist Cynthia Kuo and her colleagues conducted a study in which they gave passwords a score, with higher scores going to passwords that are not in “password crack dictionaries” that are used by hackers, that are longer, and that use a mix of letters, numbers, and symbols (2006). They...

In 2001, one county reported that among 3115 white women who had babies, 146 were multiple...

In 2001, one county reported that among 3115 white women who had babies, 146 were multiple births. There were also 22 multiple births to 647 black women. Does this indicate any racial difference in the likelihood of multiple births? a) Test an appropriate hypothesis and state your conclusion. b) If your conclusion is incorrect, which type of error did you commit? a) Let p1 be the proportion of multiple births for white women and p2 be the proportion of multiple...

In 2004, one county reported that among 3116 white women who had babies, 139 were multiple...

In 2004, one county reported that among 3116 white women who had babies, 139 were multiple births. There were also 23 multiple births to 607 black women. Does this indicate any racial difference in the likelihood of multiple births? a) Test an appropriate hypothesis and state your conclusion. b) If your conclusion is incorrect, which type of error did you commit? a) Let p1 be the proportion of multiple births for white women and p2 be the proportion of multiple...

In 2003, forty percent of the students at a major university were Business majors, 35% were...

In 2003, forty percent of the students at a major university were Business majors, 35% were Engineering majors and the rest of the students were majoring in other fields. In a sample of 600 students from the same university taken in 2004, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At 95% confidence, test to see whether there has been a significant change in the proportions between...