A random sample of 21 items is drawn from a population whose

A random sample of 21 items is drawn from a population whose standard deviation is unknown. The sample mean is x = 750 and the sample standard deviation is s = 10. Use Appendix D to find the values of Student\'s t. Construct an interval estimate of p with 98 percent confidence. Construct an interval estimate of mu with 98 percent confidence, assuming that s = 20. (Round your critical t-value to 3 decimal places. Construct an interval estimate of mu with 98 percent confidence, assuming that s = 40. Describe how the confidence interval changes as s increases.

Solution

11).

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

10

Sample Mean

750

Sample Size

21

Confidence Level

98%

Intermediate Calculations

Standard Error of the Mean

2.182178902

Degrees of Freedom

20

t Value

2.5280

Interval Half Width

5.5165

Confidence Interval

Interval Lower Limit

744.484

Interval Upper Limit

755.516

12).

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

20

Sample Mean

750

Sample Size

21

Confidence Level

98%

Intermediate Calculations

Standard Error of the Mean

4.364357805

Degrees of Freedom

20

t Value

2.5280

Interval Half Width

11.0330

Confidence Interval

Interval Lower Limit

738.967

Interval Upper Limit

761.033

13).

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation

40

Sample Mean

750

Sample Size

21

Confidence Level

98%

Intermediate Calculations

Standard Error of the Mean

8.728715609

Degrees of Freedom

20

t Value

2.5280

Interval Half Width

22.0660

Confidence Interval

Interval Lower Limit

727.934

Interval Upper Limit

772.066

14.

Interval gets wider as s increases.

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	10
Sample Mean	750
Sample Size	21
Confidence Level	98%
Intermediate Calculations
Standard Error of the Mean	2.182178902
Degrees of Freedom	20
t Value	2.5280
Interval Half Width	5.5165
Confidence Interval
Interval Lower Limit	744.484
Interval Upper Limit	755.516