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.