Question

The body mass index​ (BMI) for a sample of men and a sample of women are given below. Assume the samples are simple random samples obtained from populations with normal distributions.

Men: 22.3, 32.7, 31.1, 22.8, 32.8, 31.5, 27.7, 27.4, 31.4, 23.1

Women: 19.1, 24.8, 19.1, 34.7, 18.3, 21.9, 20.5, 33.1, 20.2, 17.8

a. Construct a 95 ​% confidence interval estimate of the standard deviation of BMIs for men.

___ < sigma Subscript men < ___ ​(Round to two decimal places as​ needed.)

b. Construct a 95 ​% confidence interval estimate of the standard deviation of BMIs for women.

___ < sigma Subscript women < ___ ​(Round to two decimal places as​ needed.)

c. Compare and interpret the results.

A. Since the intervals do not overlap ​, the populations appear to have amounts nbsp of nbspvariation nbspthat are not substantially different.

B. Since the intervals overlap ​, the populations appear to have amounts nbsp of nbspvariation nbspthat are not substantially different.

C. Since the intervals do not overlap ​, the populations appear to have different nbsp amounts nbspof nbspvariation. Your answer is correct.

D. Since the intervals overlap ​, the populations appear to have different nbsp amounts nbspof nbspvariation.

Answer 1

a) ∑x = 282.8, ∑x² = 8159.34, n = 10

Standard deviation for men, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(8159.34-(282.8)²/10)/(10-1)] = 4.2394

95% Confidence interval for population standard deviation :

df = n-1 = 9

Critical value, χ²α/2 = CHISQ.INV.RT(0.05/2, 9) = 19.0228

Critical value, χ²1-α/2 = CHISQ.INV.RT(1-0.05/2, 9) = 2.7004

b) ∑x = 229.5, ∑x² = 5603.99, n = 10

Standard deviation for women, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(5603.99-(229.5)²/10)/(10-1)] = 6.1189

95% Confidence interval for population standard deviation :

Critical value, χ²α/2 = CHISQ.INV.RT(0.05/2, 9) = 19.0228

Critical value, χ²1-α/2 = CHISQ.INV.RT(1-0.05/2, 9) = 2.7004

c. Compare and interpret the results.

C. Since the intervals do not overlap ​, the populations appear to have different amounts of variation.