Question

# A simple random sample of size n is drawn. The sample​ mean, x overbar​, is found...

A simple random sample of size n is drawn. The sample​ mean, x overbar​, is found to be 17.7​, and the sample standard​ deviation, s, is found to be 4.8.

Click the icon to view the table of areas under the​ t-distribution.

​(a) Construct a 95​% confidence interval about mu if the sample​ size, n, is 35. Lower​ bound: nothing​; Upper​ bound: nothing ​(Use ascending order. Round to two decimal places as​ needed.)

​(b) Construct a 95​% confidence interval about mu if the sample​ size, n, is 61. 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 does not change. B. The margin of error increases. C. The margin of error decreases.

​(c) Construct a 99​% confidence interval about mu if the sample​ size, n, is 35. 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​, what conditions must be satisfied to compute the confidence​ interval? A. The sample data must come from a population that is normally distributed with no outliers. B. The sample must come from a population that is normally distributed and the sample size must be large. C. The sample size must be large and the sample should not have any outliers. Click to select your answer(s).

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