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S O C A researcher is concerned with the relationship between attitudes toward violence and violent behavior. Do attitudes "cause” behavior? Do people who have positive attitudes toward violence have higher rates of violent behavior? A pretest was conducted on 70 respondents; among other things, the respondents were asked, "Have you been involved in a violent incident of any kind over the past six months?" The researcher established the following relationship: Attitude Toward Violence Involvement Favourable Unfavourable Totals Yes 16 19 35 No Totals 14 30 21 40 35 70 The chi square for this table is 0.23, which is not significant at the 0.05 level (confirm this with your own calculations). Undeterred by this result, the researcher proceeded with the project and gathered a random sample of 7000. In terms of percentage distributions, the results for the full sample were exactly the same as for the pretest: Attitude Toward Violence Involvement Favourable Unfavourable Totals Yes 1600 1900 3500 No Totals 1400 3000 2100 4000 3500 7000 However, the chi square obtained is a very healthy 23.4 (confirm with your own calculations). Why is the full-sample chi square significant when the pretest was not? What happened? Do you think that the second result is important?

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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 10, Problem 10.14P
Textbook Problem
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S O C A researcher is concerned with the relationship between attitudes toward violence and violent behavior. Do attitudes "cause” behavior? Do people who have positive attitudes toward violence have higher rates of violent behavior? A pretest was conducted on 70 respondents; among other things, the respondents were asked, "Have you been involved in a violent incident of any kind over the past six months?" The researcher established the following relationship:

Attitude Toward Violence
Involvement Favourable Unfavourable Totals
Yes 16 19 35
No
Totals
14 30 21 40 35 70

The chi square for this table is 0.23, which is not significant at the 0.05 level (confirm this with your own calculations). Undeterred by this result, the researcher proceeded with the project and gathered a random sample of 7000. In terms of percentage distributions, the results for the full sample were exactly the same as for the pretest:

Attitude Toward Violence
Involvement Favourable Unfavourable Totals
Yes 1600 1900 3500
No
Totals
1400 3000 2100 4000 3500 7000

However, the chi square obtained is a very healthy 23.4 (confirm with your own calculations). Why is the full-sample chi square significant when the pretest was not? What happened? Do you think that the second result is important?

To determine

To find:

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

Explanation of Solution

Given:

The given information is,

A researcher is concerned with the relationship between attitudes toward violence and violent behavior. A pretest was conducted on 70 respondents; among other things, the respondents were asked, "Have you been involved in a violent incident of any kind over the past six months?"

The given tables of information are,

Involvement Attitude Toward Violence
Favourable Unfavourable Totals
Yes 16 19 35
No 14 21 35
Totals 30 40 70
Involvement Attitude Toward Violence
Favourable Unfavourable Totals
Yes 1600 1900 3500
No 1400 2100 3500
Totals 3000 4000 7000

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 given tables of information for the pretest is,

Involvement Attitude Toward Violence
Favourable Unfavourable Totals
Yes 16 19 35
No 14 21 35
Totals 30 40 70

The observed frequency is given as,

fe=Rowmarginal×ColumnmarginalN……(1)

Substitute 35 for row marginal, 30 for column marginal and 70 for N in equation (1).

f1=35×3070=15

Substitute 35 for row marginal, 40 for column marginal and 70 for N in equation (1).

f2=35×4070=20

Substitute 35 for row marginal, 30 for column marginal and 70 for N in equation (1).

f3=35×3070=15

Substitute 35 for row marginal, 40 for column marginal and 70 for N in equation (1).

f4=35×4070=20

Consider the following table,

fo fe fofe (fofe)2 (fofe)2/fe
16 15 1 1 0.067
19 20 1 1 0.05
14 15 1 1 0.067
21 20 1 1 0.05
Total 70 70 0 χ2=0.23

The value fofe is obtained as,

Substitute 16 for fo and 15 for fe in the above formula.

fofe=1615=1

Squaring the above obtained result,

(fofe)2=(1)2=1

Divide the above obtained result by fe.

(fofe)2fe=115=0.067

Proceed in a similar manner to obtain rest of the values of (fofe)2/fe and refer above table for the rest of the values of (fofe)2/fe.

The chi square value is given as,

χ2(obtained)=(fofe)2fe=0.067+0.05+0.067+0.05=0.23

Thus, the chi square value is 0.23.

Follow the steps for chi square hypothesis testing.

Step 1. Making assumptions and meeting test requirements.

Model:

Independent random sampling.

Level of measurement is nominal.

Step 2. Stating the null hypothesis.

The statement of the null hypothesis is that there is no significant relationship between attitudes toward violence and involvement in a violent incident.

Thus, the null and the alternative hypotheses are,

H0: No significant relationship between attitudes toward violence and involvement in a violent incident.

H1: A significant relationship between attitudes toward violence and involvement in a violent incident.

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

The sampling distribution is chi square.

The level of significance is α=0

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