Table $1$: Correlation Matrix

Age Test Job Performance

Age $1\mathrm{.}00$

Test $0\mathrm{.}091\mathrm{.}00$

Job Performance $0\mathrm{.}200\mathrm{.}81*1\mathrm{.}00$

Note: $*$ indicates a statistical significance level of p $<\mathrm{.}05$

Table $2$: Scores Above Cutoff by Sex

Sex Above $23$ Total Count

Males $(0)1220$

Females $(1)1923$

Total $3143$

Table $3$: Scores Above Cutoff by Race

Race Above $23$ Total Count

Hispanic $(0)1518$

White $(1)1625$

Total $3143$

Questions:

$1.$ When looking at the relationship between employees$$ scores on the new cognitive ability test and their performance ratings, $($a$)$ how would you describe the relationship using what you$$ve learned in Chapter $8?($b$)$ How likely is this relationship due to chance, and how do you know this? Please explain your answer using specific numbers from the exhibits to justify your response

$2.$ Assume that the regression equation that predicts job performance using the new cognitive ability test is: $49\mathrm{.}78+(1\mathrm{.}08$ New cognitive ability test score$).$ Suppose a candidate scored $26$ on the new cognitive ability test. What is the candidate$$s predicted job performance? SHOW YOUR WORK to earn credit.

$3.$ Assume that only candidates with a score of at least $23$ on the new cognitive ability test were hired $(31$ of the $43$ people in this sample$).$ Would the use of this new cognitive ability test have led to evidence of adverse impact based on sex? SHOW YOUR WORK to earn credit.

$4.$ Would the use of this new cognitive ability test have led to evidence of adverse impact based on race? SHOW YOUR WORK to earn credit.

$5.$ Based on your analyses, would you recommend use of this new cognitive ability test as a selection device? If so$,$ why would you use it and how would you use it as part of the selection process? If you would not use it$,$ why? Please justify your response using what you$$ve learned in class.