The following four
HINTS:
• Calculate the expected frequencies for each cell with Formula 10.2. Double check to make sure you are using the correct row and column marginals for each cell.
• It may he helpful to record the expected frequencies in table format—see Tables 10.4 and 10.8.
• Use a computational table to organize the calculation for Formula 10.1—see Tables 10.5 and 10.9.
• Follow the stepbystep instructions.
• Doublecheck to make sure you are using the correct values for each cell.
a. 



c. 










b. 



d. 









(a)
To find:
The chi square value for the given information.
Solution:
The chi square value is 1.12.
Given:
The given table of information is,
a.  
Description:
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.
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
Calculation:
From the given information,
The row marginal is 45, the column marginal is 45 and N is 90.
The observed frequency is given as,
Substitute 45 for row marginal, 45 for column marginal and 90 for N in the above formula.
Consider the following table,
20  22.5  0.28  
25  22.5  0.28  
25  22.5  0.28  
20  22.5  0.28  
Total  90  90  0 
The value
Substitute 20 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 1.12.
Conclusion:
The chi square value is 1.12.
(b)
To find:
The chi square value for the given information.
Solution:
The chi square value is 0.0.
Given:
The given table of information is,
b.  10  15  25 
20  30  50  
30  45  75 
Description:
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.
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
Calculation:
From the given information,
The observed frequency is given as,
Substitute 25 for row marginal, 30 for column marginal and 75 for N in equation
Substitute 25 for row marginal, 45 for column marginal and 75 for N in equation
Substitute 50 for row marginal, 30 for column marginal and 75 for N in equation
Substitute 50 for row marginal, 45 for column marginal and 75 for N in equation
Consider the following table,
10  10  0  0  0  
15  15  0  0  0  
20  20  0  0  0  
30  30  0  0  0  
Total  75  75  0  0 
The value
Substitute 10 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 0.0.
Conclusion:
The chi square value is 0.0.
(c)
To find:
The chi square value for the given information.
Solution:
The chi square value is 1.51.
Given:
The given table of information is,
c.  25  15  40 
30  30  60  
55  45  100 
Description:
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.
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
Calculation:
From the given information,
The observed frequency is given as,
Substitute 40 for row marginal, 55 for column marginal and 100 for N in equation
Substitute 40 for row marginal, 45 for column marginal and 100 for N in equation
Substitute 60 for row marginal, 55 for column marginal and 100 for N in equation
Substitute 60 for row marginal, 45 for column marginal and 100 for N in equation
Consider the following table,
25  22  3  9  0.41  
15  18  9  0.50  
30  33  9  0.27  
30  27  3  9  0.33  
Total  100  100  0 
The value
Substitute 25 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 1.51.
Conclusion:
The chi square value is 1.51.
(d)
To find:
The chi square value for the given information.
Solution:
The chi square value is 1.43.
Given:
The given table of information is,
d.  20  45  65 
15  20  35  
35  65  100 
Description:
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.
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
Calculation:
From the given information,
The observed frequency is given as,
Substitute 65 for row marginal, 35 for column marginal and 100 for N in equation
Substitute 65 for row marginal, 65 for column marginal and 100 for N in equation
Substitute 35 for row marginal, 35 for column marginal and 100 for N in equation
Substitute 35 for row marginal, 65 for column marginal and 100 for N in equation
Consider the following table,
20  22.75  2.75  7.5625  0.332417582  
45  42.25  2.75  7.5625  0.178994083  
15  12.25  2.75  7.5625  0.617346939  
20  22.75  7.5625  0.332417582  
Total  100  100  0 
The value
Substitute 20 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 1.46.
Conclusion:
The chi square value is 1.46.
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