Question

A simple random sample of size n is drawn. The sample​ mean, x overbarx​, is found to be 19.219.2​, and the sample standard​ deviation, s, is found to be 4.34.3. LOADING... Click the icon to view the table of areas under the​ t-distribution. ​(a) Construct a 9595​% confidence interval about muμ if the sample​ size, n, is 3535. Lower​ bound: nothingm​; Upper​ bound: nothingm ​(Use ascending order. Round to two decimal places as​ needed.) ​(b) Construct a 9595​% confidence interval about muμ if the sample​ size, n, is 6161. Lower​ bound: nothingm​; Upper​ bound: nothingm ​(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 9999​% confidence interval about muμ if the sample​ size, n, is 3535. Lower​ bound: nothingm​; Upper​ bound: nothingm ​(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 decreases. B. The margin of error increases. C. The margin of error does not change. ​(d) If the sample size is 1515​, what conditions must be satisfied to compute the confidence​ interval? A. The sample size must be large and the sample should not have any outliers. B. The sample must come from a population that is normally distributed and the sample size must be large. C. The sample data must come from a population that is normally distributed with no outliers.

Answer 1

a) At 95% confidence interval the critical value is t^* = 2.032

The 95% confidence interval is

+/- t^* * s/

= 19.2 +/- 2.032 * 4.3/

= 19.2 +/- 1.48

= 17.72, 20.68

b) At 95% confidence interval the critical value is t^* = 2.000

The 95% confidence interval is

+/- t^* * s/

= 19.2 +/- 2 * 4.3/

= 19.2 +/- 1.45

= 17.75, 20.65

Option -C) The margin of error decreases.

c) At 99% confidence interval the critical value is t^* = 2.728

The 99% confidence interval is

+/- t^* * s/

= 19.2 +/- 2.728 * 4.3/

= 19.2 +/- 1.98

= 17.22, 21.18

Option - B) the margin of error increases.

d) Option - C) The sample data must come from a population that is normally distributed with no outliers.