Central Middle School has calculated a 95% confidence interval for the mean height (μ) of11-year-old boys at their school and found it to be 56 ± 2 inches.(a) Determine whether each of the following statements is true or false.• There is a 95% probability that μ is between 54 and 58.• There is a 95% probability that the true mean is 56, and there is a 95% chance thatthe true margin of error is 2.• If we took many additional random samples of the same size and from eachcomputed a 95% confidence interval for μ, approximately 95% of these intervalswould contain μ.• If we took many additional random samples of the same size and from eachcomputed a 95% confidence interval for μ, approximately 95% of the time μwould fall between 54 and 58.(b) Which of the following could be the 90% confidence interval based on the same data?• 56 ± 1• 56 ± 2• 56 ± 3• Without knowing the sample size, any of the above answers could be the 90%confidence interval.
Central Middle School has calculated a 95% confidence interval for the mean height (μ) of
11-year-old boys at their school and found it to be 56 ± 2 inches.
(a) Determine whether each of the following statements is true or false.
• There is a 95%
• There is a 95% probability that the true mean is 56, and there is a 95% chance that
the true margin of error is 2.
• If we took many additional random samples of the same size and from each
computed a 95% confidence interval for μ, approximately 95% of these intervals
would contain μ.
• If we took many additional random samples of the same size and from each
computed a 95% confidence interval for μ, approximately 95% of the time μ
would fall between 54 and 58.
(b) Which of the following could be the 90% confidence interval based on the same data?
• 56 ± 1
• 56 ± 2
• 56 ± 3
• Without knowing the sample size, any of the above answers could be the 90%
confidence interval.
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