a.
To find:
Effect on margin of error for confidence interval for a population
Answer to Problem 22E
Solution:
When the sample size decreases, there is an increase in the margin of error for a population mean.
Explanation of Solution
Given:
The sample size decreases from
Description:
Given a population with standard deviation
The true population parameters probability lies in this interval range is known as the confidence level
At a certain level of confidence, the interval in which the maximum error can be observed is known as the confidence interval.
The maximum distance from point estimate that the confidence interval covers is margin of error and is given by:
where,
Calculation:
Thus, the ratio of margins of error is:
where
The ratio is calculated as follows:
which gives:
Conclusion:
When the sample size decreases, there is an increase in the margin of error for a population mean.
b.
To find:
Effect on width of confidence interval for a population mean if sample size decreases from 500 to 387 people.
Answer to Problem 22E
Solution:
When the sample size decreases, there is an increase in the width of confidence interval for a population mean.
Explanation of Solution
Given:
The sample size decreases from
Description:
Given a population with standard deviation
The true population parameters probability lies in this interval range is known as the confidence level
At a certain level of confidence, the interval in which the maximum error can be observed is known as the confidence interval.
The maximum distance from point estimate that the confidence interval covers is margin of error and is given by:
where,
Given the sample mean
and width of confidence interval is:
Calculation:
Thus, the ratio of widths of respective confidence intervals is:
where
The ratio is calculated as follows:
which gives:
Conclusion:
When the sample size decreases, there is an increase in the width of confidence interval for a population mean.
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Chapter 8 Solutions
Beginning Statistics, 2nd Edition
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