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P A All applicants to the Police Academy are given an aptitude test, but the test has never been evaluated to see if test scores are in any way related to job performance. Describe the strength and direction of the relationship in a sentence or two. Should the test continue to be administered? Why or why not? Efficiency Test Scores Low Moderate High Totals Low 12 6 7 25 Moderate 9 11 9 29 High Totals 5 26 9 26 10 26 24 78

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Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

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Chapter
Section
BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 11, Problem 11.8P
Textbook Problem
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P A All applicants to the Police Academy are given an aptitude test, but the test has never been evaluated to see if test scores are in any way related to job performance. Describe the strength and direction of the relationship in a sentence or two. Should the test continue to be administered? Why or why not?

Efficiency Test Scores
Low Moderate High Totals
Low 12 6 7 25
Moderate 9 11 9 29
High
Totals
5 26 9 26 10 26 24 78

To determine

To find:

The strength and pattern of relationship.

Explanation of Solution

Given:

The given statement is,

All applicants to the Police Academy are given an aptitude test, but the test has never been evaluated to see if test scores are in any way related to job performance.

The given table of information is,

Efficiency Test Scores
Low Moderate High Totals
Low 12 6 7 25
Moderate 9 11 9 29
High 5 9 10 24
Totals 26 26 26 78

Approach:

If the gamma value is less than 0.30, it is said that there is a weak association between the categories.

If the gamma value is greater than 0.60, it is said that there is a strong association between the categories.

The gamma compares the number of pairs of cases ranked in the same order on both variables (Ns) with the number of cases ranked in different order (Nd).

Formula used:

For compares the number of pairs of cases ranked in the same order on both variables (Ns) with the number of cases ranked in different order (Nd) the gamma G is given as,

G=NsNdNs+Nd

Calculation:

From the given table of information,

The value of Ns is computed as,

Ns=12(11+9+9+10)+6(9+10)+9(9+10)+11(10)=863

And the value of Nd is computed as,

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