Question

The diameters​ (in inches) of 17 randomly selected bolts produced by a machine are listed. Use a 99​%

level of confidence to construct a confidence interval for ​(a) the population variance sigma squared σ2 and ​(b) the population standard deviation sigmaσ. Interpret the results.

4.466
3.805
3.945
4.419
3.772
3.755
4.022
4.247
3.847
4.325
3.976
3.806
4.008
4.154
4.472
3.786
4.573

a) The confidence interval for the population variance is​( FILL IN ​, FILL IN ​). ​(Round to three decimal places as​ needed.) Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to three decimal places as​ needed.) A.With 99% ​confidence, it can be said that the population variance is greater than (FILL IN IF ANSWER ). B.With 99% ​confidence, it can be said that the population variance is between BLANK and BLANK .C.With 1​% ​confidence, it can be said that the population variance is between BLANK and BLANK . D.With 1​% ​confidence, it can be said that the population variance is less than Fill IN IF ANSWER . ​(b) The confidence interval for the population standard deviation is (FILL IN, FILL IN ) ​(Round to three decimal places as​ needed.) Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to three decimal place as​ needed.) A.With 99​% ​confidence, you can say that the population standard deviation is less than (Fill in if answer ) inches. B.With 1​% ​confidence, you can say that the population standard deviation is greater than (Fill in if answer ) inches. C. With 99% ​confidence, you can say that the population standard deviation is between (Blank and Blank ) inches. D.With 1​% ​confidence, you can say that the population standard deviation is between (BLANK AND BLANK) inches

Answer 1

The diameters​ (in inches) of 17 randomly selected bolts produced by a machine are listed. Use a 99​%level of confidence to construct a confidence interval for ​(a) the population variance sigma squared σ2 and ​(b) the population standard deviation sigmaσ. Interpret the results.

Descriptive Summary
	Diameter
Mean	4.0811
Variance	0.0802
Standard Deviation	0.2832

The confidence interval for the population variance is​( 0.037, 0.250 ​). ​(Round to three decimal places as​ needed.)

Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to three decimal places as​ needed.)

B.With 99% ​confidence, it can be said that the population variance is between 0.037 and 0.250 .

​

(b) The confidence interval for the population standard deviation is (0.194, 0.500 ) ​(Round to three decimal places as​ needed.)

Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to three decimal place as​ needed.)

C. With 99% ​confidence, you can say that the population standard deviation is between (0.194 and 0.500 ) inches.

CI for variance

Confidence Interval Estimate for the Population Variance
Data
Sample Size	17
Sample Standard Deviation	0.2832
Confidence Level	99%
Intermediate Calculations
Degrees of Freedom	16
Sum of Squares	1.28323584
Single Tail Area	0.005
Lower Chi-Square Value	5.1422
Upper Chi-Square Value	34.2672
Results
Interval Lower Limit for Variance	0.037
Interval Upper Limit for Variance	0.250
Interval Lower Limit for Standard Deviation	0.194
Interval Upper Limit for Standard Deviation	0.500