i.
No of degrees of freedom associated with
i.
Answer to Problem 14.18E
No of degrees of freedom associated with
Explanation of Solution
Given:
Columns | ||||
Rows | Total | |||
Total |
Formula Used:
Degrees of freedom for contingency table:
Calculation:
Consider null and alternative hypothesis.
Null hypothesis,
Alternative hypothesis,
To find degrees of freedom for contingency table:
Where,
So, the contingency table contains two rows and three columns.
Degree of freedom,
Thus,
Conclusion:
Thus, no. of degrees of freedom associated with
ii.
To find: the value of test statistic.
ii.
Answer to Problem 14.18E
The value of test statistic is
Explanation of Solution
Given:
Columns | ||||
Rows | Total | |||
Total |
Formula Used:
Test statistic:
Where,
Calculation:
Observed | Expected | |||
From the above table, the test statistic which is observed is
Conclusion:
Thus,
iii.
To find:
Rejection region for
iii.
Answer to Problem 14.18E
the test statistic
Explanation of Solution
Given:
Columns | ||||
Rows | Total | |||
Total |
Calculation:
The given level of significance
The rejection region,
The critical value with
Conclusion:
Thus, the rejection region
iv.
To identify: test and its conclusion.
iv.
Answer to Problem 14.18E
The probability that a response falls in any row is independent of the columns if falls in.
Explanation of Solution
Given:
Columns | ||||
Rows | Total | |||
Total |
Calculation:
For getting test initially compare the calculated value with the critical value.
By using the rejection region, the calculated value of test statistic less than the level of significance than fails to reject the null hypothesis.
Conclusion:
Thus, the probability that a response falls in any row is independent of the columns if falls in.
v.
To identify: The P-value for the test.
v.
Answer to Problem 14.18E
The P-value for the test is
Explanation of Solution
Given:
Columns | ||||
Rows | Total | |||
Total |
Calculation:
Critical value is calculated as:
P-value
So, here
Conclusion:
Thus, the required P-value is
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Chapter 14 Solutions
Introduction to Probability and Statistics
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