SOLUTION: 4. A simple random sample of size n is drawn. The sample​ mean, x overbar​, is found to be18.1​, and the sample standard​ deviation, s, is found to be 4.9. 1 Click the

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Question 1135049: 4.
A simple random sample of size n is drawn. The sample​ mean,
x overbar​, is found to be18.1​, and the sample standard​ deviation, s, is found to be 4.9.
1 Click the icon to view the table of areas under the​ t-distribution.
​(a) Construct a 95​% confidence interval about
mu μ if the sample​ size, n, is 34.
Lower​ bound:______ ​; Upper​ bound: _____
​(Use ascending order. Round to two decimal places as​ needed.)
​(b) Construct a 95​% confidence interval about
mu μ if the sample​ size, n, is 51.
Lower​ bound:
nothing
​; Upper​ bound:
nothing
​(Use ascending order. Round to two decimal places as​ needed.)
How does increasing the sample size affect the margin of​ error, E?
A.
The margin of error increases.
B.
The margin of error does not change.
C.
The margin of error decreases.
​(c) Construct a 99​% confidence interval about
mu μ if the sample​ size, n, is 34.
Lower​ bound:
nothing
​; Upper​ bound:
nothing
​(Use ascending order. Round to two decimal places as​ needed.)
Compare the results to those obtained in part​ (a). How does increasing the level of confidence affect the size of the margin of​ error, E?
A.
The margin of error increases.
B.
The margin of error does not change.
C.
The margin of error decreases.
​(d) If the sample size is
12
12​, what conditions must be satisfied to compute the confidence​ interval?
A.
The sample must come from a population that is normally distributed and the sample size must be large.
B.
The sample data must come from a population that is normally distributed with no outliers.
C.
The sample size must be large and the sample should not have any outliers.



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