Concept explainers
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 step-by-step instructions.
• Double-check to make sure you are using the correct values for each cell.
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(a)
To find:
The chi square value for the given information.
Answer to Problem 10.1P
Solution:
The chi square value is 1.12.
Explanation of Solution
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.
Answer to Problem 10.1P
Solution:
The chi square value is 0.0.
Explanation of Solution
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.
Answer to Problem 10.1P
Solution:
The chi square value is 1.51.
Explanation of Solution
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.
Answer to Problem 10.1P
Solution:
The chi square value is 1.43.
Explanation of Solution
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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