Concept explainers
Section 1
To find: The 70% confidence interval for the proportion of American adults who reported looking for information on food labels about whether the food they are purchasing is organic.
Answer to Problem 29E
Solution: The confidence interval is
Explanation of Solution
Calculation:
Compute the confidence interval using formula as follows:
where
Now, compute the 70% confidence interval as follows:
Interpretation: It can be concluded with 70% confidence that proportion of American adults who reported looking for information on food labels about whether the food they are purchasing is organic lies between 47.4% and 50.6%.
Section 2
To find: The 80% confidence interval for the proportion of American adults who reported looking for information on food labels about whether the food they are purchasing is organic.
Solution: The confidence interval is
Explanation:
Calculation:
Compute the confidence interval using formula as follows:
where
Now, compute the 80% confidence interval as follows:
Interpretation: It can be concluded with 80% confidence that proportion of American adults who reported looking for information on food labels about whether the food they are purchasing is organic lies between 47% and 51%.
Section 3
To find: The 90% confidence interval for the proportion of American adults who reported looking for information on food labels about whether the food they are purchasing is organic.
Solution: The confidence interval is
Explanation:
Calculation:
Compute the confidence interval using formula as follows:
where
Now, compute the 90% confidence interval as follows:
Interpretation: It can be concluded with 90% confidence that proportion of American adults who reported looking for information on food labels about whether the food they are purchasing is organic lies between 46% and 52%.
Section 4
To find: The 99% confidence interval for the proportion of American adults who reported looking for information on food labels about whether the food they are purchasing is organic.
Solution: The confidence interval is
Explanation:
Calculation:
Compute the confidence interval using formula as follows:
where
Now, compute the 99% confidence interval as follows:
Interpretation: It can be concluded with 99% confidence that proportion of American adults who reported looking for information on food labels about whether the food they are purchasing is organic lies between 45% and 53%.
Section 5
To find: The comparison of confidence intervals obtained in sections 1, 2, 3, and 4.
Solution: The width of confidence interval widens with increase in confidence level.
Explanation:
Calculation:
Now, compute the width of the 70%, 80%, 90%, and 99% confidence intervals.
The width of 70% confidence interval is calculated as shown below:
The width of 80% confidence interval is calculated as shown below:
The width of 90% confidence interval is calculated as shown below:
The width of 99% confidence interval is calculated as shown below:
From the above calculations, it is clear that if there is an increase in the confidence level, then there is an increase in the width of the confidence interval.
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Chapter 21 Solutions
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