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To build and to interpret:
A
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Answer to Problem 24E
Solution:
The confidence interval for the population variance is given by (0.0019, 0.0128).
Thus, we are 98% confident that the population variance is between 0.0019 and 0.0128.
Explanation of Solution
Procedure:
Steps need to be followed while calculating the confidence interval.
STEP 1:
Find the point estimate,
STEP 2:
Calculate
STEP 3:
Find the critical value
STEP 4:
Find the confidence interval for the population variance by substituting the necessary values in the formula
Find the confidence interval for the population standard deviation by substituting the necessary values in the formula
Calculation:
Level confidence =98%
First let us calculate the sample variance for the given data.
The sample variance of a data having ‘n’ number of data values in the sample with mean ‘
Here, we need to find the mean ‘
Now, construct a table of deviations and squared deviations of the data.
Deviations and squared Deviations of the data | ||
Thus, we have
Substituting the above values in
Now, construct a confidence interval for the population variance with
STEP 1:
Find the point estimate:
Here, we need to construct the confidence interval for the population variance, thus the point estimate is the value of
STEP 2:
Calculate
We have,
Thus,
STEP 3:
Find the critical value
STEP 4:
Find the confidence interval by substituting the necessary values in the formula:
Using, interval notation, the confidence interval can also be written as (0.0019, 0.0128)
Final statement:
Therefore, the confidence interval for the population variance is given by (0.0019, 0.0128).
Thus, we are 98% confident that the population variance is between 0.0019 and 0.0128.
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Chapter 8 Solutions
Beginning Statistics, 2nd Edition
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