Concept explainers
(a)
Explain themargin of errorwhen the confidence level is 95%.
(a)
Answer to Problem 11E
The margin of error is 3% when the confidence level of 95% for all sample.
Explanation of Solution
Given information:
Sample proportion = 66%
Confidence level = 95%
Margin of error for the confidence level = 3%
The margin of error is a statistic measurement that gives the amount of the random sampling error in the result of a survey. Higher the margin of error, the less confidence level would reflect the result of a survey of the entire population.
Hence, themargin of erroris 3% when the confidence level of 95% for all sample.
(b)
To calculate:The true population proportion contain by the confidence interval.
(b)
Answer to Problem 11E
The true population proportion contain by the confidence interval is from 0.63 to 0.69.
Explanation of Solution
Given information:
Sample proportion = 66%
Confidence level = 95%
Margin of error for the confidence level = 3%
Sample proportion
Convert 66% into decimal.
Margin of error
Convert 3% into decimal
The sample proportion can vary by the amount margin of error. Thus, the confidence that contain true proportion also vary from minimum to maximum sample proportion.
Hence,the true population proportion contain by the confidence interval is from 0.63 to 0.69.
(c)
Explain the confidence level that contains true population proportion.
(c)
Answer to Problem 11E
95% of the confidence interval has the true population proportion.
Explanation of Solution
Given information:
Sample proportion = 66%
Confidence level = 95%
Margin of error for the confidence level = 3%
Confidence level is the probability that the value of a parameter falls within a specified
Hence, 95% of theconfidence interval has the true population proportion.
Chapter 8 Solutions
The Practice of Statistics for AP - 4th Edition
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