Question

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

99​% confidence interval estimate of the population standard deviation. USE CHI -SQAURE CRITICAL VALUES

62

63

63

55

63

53

59

58

59

69

58

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. 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.

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

Answer 1

We need to calculate the sd of the given data:

	speed	x^2
	62	3844
	63	3969
	63	3969
	55	3025
	63	3969
	53	2809
	59	3481
	58	3364
	59	3481
	69	4761
	58	3364
	67	4489
Total	729	44525

The sample variance is given by the formula:

The sample size is given by n=12.

The 99% confidence interval for variance is given by

Therefore the 99% confidence interval for the SD is

The confidence interval estimate is 3.0 mi/h <σ< 9.6 ​mi/h

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

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