A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 109, and the sample standard deviation, s, is found to be 10.
(a) Construct a 98% confidence interval about μ if the sample size, n, is 22.
(b) Construct a 98% confidence interval about μ if the sample size, n, is 12.
(c) Construct a 70% confidence interval about μ if the sample size, n, is 22.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
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Part 1
(a) Construct a 98% confidence interval about μ if the sample size, n, is 22.
Lower bound: enter your response here; Upper bound: enter your response here
(Use ascending order. Round to one decimal place as needed.)
Part 2
(b) Construct a 98% confidence interval about μ if the sample size, n, is 12.
Lower bound: enter your response here; Upper bound: enter your response here
(Use ascending order. Round to one decimal place as needed.)
Part 3
How does decreasing the sample size affect the margin of error, E?
A.
As the sample size decreases, the margin of error increases.
B.
As the sample size decreases, the margin of error decreases.
C.
As the sample size decreases, the margin of error stays the same.
Part 4
(c) Construct a 70% confidence interval about μ if the sample size, n, is 22.