Concept explainers
(a)
Explain the margin of error when the confidence level is 95%.
(a)
Answer to Problem 12E
The margin of error is 3% when the confidence level of 95% for all sample.
Explanation of Solution
Given information:
Sample proportion = 59%
Confidence level = 95%
Margin of error = 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, the margin of error is 3% for the confidence level of 95% for all sample.
(b)
To calculate: the true population proportion contain by the confidence interval.
(b)
Answer to Problem 12E
The true population proportion contain by the confidence interval is from 0.63 to 0.69.
Explanation of Solution
Given information:
Sample proportion = 59%
Confidence level = 95%
Margin of error = 3%
Sample proportion=
Convert percentage into decimal
Margin of error=
Convert percentage 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 amount of confidence interval that contain the true population proportion is from 0.56 to 0.62.
(c)
Explain the confidence level.
(c)
Answer to Problem 12E
95% 0f the confidence interval has the true population proportion.
Explanation of Solution
Given information:
Sample proportion = 59%
Confidence level = 95%
Margin of error = 3%
Confidence level is the probability that the value of a parameter falls within a specified
Hence, the confidence interval has the true population proportion for all sample is 95%.
Chapter 8 Solutions
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