Question

9. Use the given information to find the number of degrees of​ freedom, the critical values X2/L​, and X2/R and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Nicotine in menthol cigarettes 90​% ​confidence; n=21​, s=0.25 mg.

Df=_____

​(Type a whole​ number.)

X2/L=_____

Round to three decimal places as​ needed.)

X2/R=____

​(Round to three decimal places as​ needed.)

The confidence interval estimate of σ is ____ mg < σ <____mg.

​(Round to two decimal places as​ needed.)

10. Listed below are speeds​ (mi/h) measured from traffic on a busy highway. This simple random sample was obtained at​ 3:30 P.M. on a weekday. Use the sample data to construct a 98​% confidence interval estimate of the population standard deviation.

64, 63, 63, 57, 63, 52, 60, 59,60, 70, 59, 67

The confidence interval estimate is ____mi/h < σ <___mi/h

​(Round to one decimal place as​ needed.)

Does the confidence interval describe the standard deviation for all times during the​ week? Choose the correct answer below.

A.Yes. The confidence interval describes the standard deviation for all times during the week.

B.No. The confidence interval is an estimate of the standard deviation of the population of speeds at​ 3:30 on a​ weekday, not other times.

Answer 1

Question 9

Degree of freedom = n - 1 = 21 - 1 = 20

X2/L= 10.851

X2/R= 31.410

χ² (0.1/2) = 31.4104
χ² (1 - 0.1/2) ) = 10.8508
Lower Limit = (( 21-1 ) 0.0625 / χ² (0.1/2) ) = 0.0398
Upper Limit = (( 21-1 ) 0.0625 / χ² (0.1/2) ) = 0.1152
90% Confidence interval is ( 0.0398 , 0.1152 )
( 0.04 < σ² < 0.12 )
( 0.20 < σ < 0.34 )

Question 10

	Values ( X )	Σ ( Xi- X̅ )2
	64	6.6734
	63	2.5068
	63	2.5068
	57	19.5072
	63	2.5068
	52	88.6742
	60	2.007
	59	5.8404
	60	2.007
	70	73.673
	59	5.8404
	67	31.1732
Total	737.0	242.9162

Mean X̅ = Σ Xi / n
X̅ = 737 / 12 = 61.4167
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 242.9162 / 12 -1 ) = 4.6993

χ² (0.02/2) = 24.725
χ² (1 - 0.02/2) ) = 3.0535
Lower Limit = (( 12-1 ) 22.0834 / χ2 (0.02/2) ) = 9.8248
Upper Limit = (( 12-1 ) 22.0834 / χ² (0.02/2) ) = 79.5538
98% Confidence interval is ( 9.8248 , 79.5538 )
( 9.8 < σ² < 79.6 )
( 3.1 < σ < 8.9 )

B.No. The confidence interval is an estimate of the standard deviation of the population of speeds at​ 3:30 on a​ weekday, not other times.