According to extant evidence, the effect of arresting domestic offenders on thei

Question

According to extant evidence, the effect of arresting domestic offenders on their recidivism is inconsistent. You conducted your own research using a sample of 270 domestic offenders and found the following results:

Recidivism Increased

Recidivism Decreased

Did Not Recidivate

105

95

70

Use the above data to answer questions 2a through 2f
2a) State the null and research hypotheses (2 points)
2b) Indicate the appropriate statistical test (1 point)
2c) With the significance level set at .01, specify your critical value (3 points)
2d) Report the obtained value (5 points)
2e) Declare your decision (i.e., whether to reject or retain the H0; 2 points).
2f) What can you conclude in terms of the observed frequencies in recidivism among the three categories of domestic violence offenders (2 points)?

Recidivism Increased

Recidivism Decreased

Did Not Recidivate

105

95

70

Explanation / Answer

Given table data is as below

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Recidivism Increased, 105

Recidivism Decreased, 95

Did Not Recidivate,70

calculation formula for E table matrix

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E = 270/3 = 90

calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as

null, Ho: no association b/w them OR effect of arresting domestic offenders on their recidivism is inconsistent

alternative, H1: association b/w them OR not Ho.

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =11.34

since our test is right tailed,reject Ho when ^2 o > 11.34

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table , ^2 o = 7.22

critical value

the value of |^2 | at los 0.05 with d.f 3 -1 = 2 is 11.34

we got | ^2| =7.22 & | ^2 | =11.34

make decision

hence value of | ^2 o | > | ^2 | and here we don't reject Ho

ANSWERS

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a.null, Ho: no association b/w them

alternative, H1: association b/w them OR not Ho

b. Chi square test for independence

c. critical value: 11.34

d. test statistic: 7.22

e. decision: reject Ho

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