To construct and interpret the specified confidence interval
A tire manufacture is testing the tire pressure in its new line of SUV tires. A random sample of
Answer to Problem 18E
Solution:
The confidence interval for the population variance is given by
The manufacturer can be 95% confident that the variance in pressure of all the new SUV tires is between 16.9 psi and 106 psi.
Explanation of Solution
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:
Given,
A sample of
Thus,
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
For the level of confidence given,
We have
Thus,
STEP 3:
Find the critical value
Find the confidence interval by substituting the necessary values in the formula.
Using, interval notation, the confidence interval can also be written as
Final statement:
Therefore, the confidence interval for the population variance is given by
The manufacturer can be 95% confident that the variance in pressure of all the new SUV tires is between 16.9 psi and 106 psi.
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Chapter 8 Solutions
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