   # C J A local judge has been allowing some individuals convicted of “driving under the influence” to work in a hospital emergency room as an alternative to fines, suspensions, and other penalties. A random sample of offenders has been drawn. Do participants in this program have lower rates of recidivism for this offense? Explain your results in a sentence or two, citing both the results of the chi square test and the patterns of the column percentages. Recidivist? Status Nonparticipant Participant Totals Yes 60 123 183 No Totals 55 115 108 231 163 346 ### Essentials Of Statistics

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

#### Solutions

Chapter
Section ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 10, Problem 10.6P
Textbook Problem
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## C J A local judge has been allowing some individuals convicted of “driving under the influence” to work in a hospital emergency room as an alternative to fines, suspensions, and other penalties. A random sample of offenders has been drawn. Do participants in this program have lower rates of recidivism for this offense? Explain your results in a sentence or two, citing both the results of the chi square test and the patterns of the column percentages. Recidivist? Status Nonparticipant Participant Totals Yes 60 123 183 NoTotals 55 115 108 231 163 346

To determine

To find:

The chi square value for the given information and test for its significance.

### Explanation of Solution

Given:

The given statement is,

A local judge has been allowing some individuals convicted of “driving under the influence” to work in a hospital emergency room as an alternative to fines, suspensions, and other penalties. A random sample of offenders has been drawn.

The given table of information is,

 Recidivist? Status Nonparticipants Participant Totals Yes 60 123 183 No 55 108 163 Totals 115 231 346

Approach:

The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.

The five step model for hypothesis testing is,

Step 1. Making assumptions and meeting test requirements.

Step 2. Stating the null hypothesis.

Step 3. Selecting the sampling distribution and establishing the critical region.

Step 4. Computing test statistics.

Step 5. Making a decision and interpreting the results of the test.

Formula used:

For a chi square, the expected frequency fe is given as,

fe=Rowmarginal×ColumnmarginalN

Where N is the total of frequencies.

The chi square statistic is given by,

χ2(obtained)=(fofe)2fe

Where fo is the observed frequency,

And fe is the expected frequency.

The degrees of freedom for the bivariate table is given as,

df=(r1)(c1)

Where r is the number of rows and c is the number of columns.

Calculation:

From the given information,

The observed frequency is given as,

fe=Rowmarginal×ColumnmarginalN……(1)

Substitute 183 for row marginal, 115 for column marginal and 346 for N in equation (1).

f1=183×115346=60.82

Substitute 183 for row marginal, 231 for column marginal and 346 for N in equation (1).

f2=183×231346=122.18

Substitute 163 for row marginal, 115 for column marginal and 346 for N in equation (1).

f3=163×115346=54.18

Substitute 163 for row marginal, 231 for column marginal and 346 for N in equation (1).

f4=163×231346=108.82

Consider the following table,

 6.25 fo fe fo−fe (fo−fe)2 (fo−fe)2/fe 60 60.82 −0.82 0.67 0.011 123 122.18 0.82 0.67 0.006 55 54.18 0.82 0.67 0.012 108 108.82 −0.82 0.67 0

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