Question

A simple random sample of size n is drawn. The sample​ mean, x overbarx​, is found to be 19.519.5​, and the sample standard​ deviation, s, is found to be 4.24.2. 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 3434. Lower​ bound: 18.0318.03​; Upper​ bound: 20.9720.97 ​(Use ascending order. Round to two decimal places as​ needed.) ​(b) Construct a 9595​% confidence interval about muμ if the sample​ size, n, is 5151. 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 decreases. C. The margin of error increases. ​(c) Construct a 9999​% confidence interval about muμ if the sample​ size, n, is 3434. 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 decreases. B. The margin of error does not change. C. The margin of error increases. ​(d) If the sample size is 1515​, 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

Answer 1

Answer:

A simple random sample of size n is drawn. The sample​ mean, x overbarx​, is found to be 19.5​, and the sample standard​ deviation, s, is found to be 4.2. LOADING... Click the icon to view the table of areas under the​ t-distribution.

​(a) Construct a 95​% confidence interval about muμ if the sample​ size, n, is 34.

Lower​ bound: 18.03​; Upper​ bound: 20.97 ​(Use ascending order. Round to two decimal places as​ needed.)

​(b) Construct a 95​% confidence interval about muμ if the sample​ size, n, is 51.

Lower​ bound: 18.32 ​; Upper​ bound: 20.68 ​(Use ascending order. Round to two decimal places as​ needed.)

How does increasing the sample size affect the margin of​ error, E?

B. The margin of error decreases.

(c) Construct a 99​% confidence interval about muμ if the sample​ size, n, is 34.

Lower​ bound: 17.53​; Upper​ bound: 21.47 ​(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?

C. The margin of error increases.

​(d) If the sample size is 15​, 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.

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	4.2
Sample Mean	19.5
Sample Size	34
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.720294058
Degrees of Freedom	33
t Value	2.0345
Interval Half Width	1.4654
Confidence Interval
Interval Lower Limit	18.03
Interval Upper Limit	20.97

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	4.2
Sample Mean	19.5
Sample Size	51
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.588117635
Degrees of Freedom	50
t Value	2.0086
Interval Half Width	1.1813
Confidence Interval
Interval Lower Limit	18.32
Interval Upper Limit	20.68

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	4.2
Sample Mean	19.5
Sample Size	34
Confidence Level	99%
Intermediate Calculations
Standard Error of the Mean	0.720294058
Degrees of Freedom	33
t Value	2.7333
Interval Half Width	1.9688
Confidence Interval
Interval Lower Limit	17.53
Interval Upper Limit	21.47