Attitude Toward Violence  
Involvement  Favourable  Unfavourable  Totals 
Yes  16  19  35 
No Totals 



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 



However, the chi square obtained is a very healthy 23.4 (confirm with your own calculations). Why is the fullsample chi square significant when the pretest was not? What happened? Do you think that the second result is important?
To find:
The chi square value for the given information and test for its significance.
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
Where N is the total of frequencies.
The chi square statistic is given by,
Where
And
The degrees of freedom for the bivariate table is given as,
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,
Substitute 35 for row marginal, 30 for column marginal and 70 for N in equation
Substitute 35 for row marginal, 40 for column marginal and 70 for N in equation
Substitute 35 for row marginal, 30 for column marginal and 70 for N in equation
Substitute 35 for row marginal, 40 for column marginal and 70 for N in equation
Consider the following table,
16  15  1  1  0.067  
19  20  1  0.05  
14  15  1  0.067  
21  20  1  1  0.05  
Total  70  70  0 
The value
Substitute 16 for
Squaring the above obtained result,
Divide the above obtained result by
Proceed in a similar manner to obtain rest of the values of
The chi square value is given as,
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,
Step 3. Selecting the sampling distribution and establishing the critical region.
The sampling distribution is chi square.
The level of significance is
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