Question

The body mass index for a sample of men and a sample of women are given below. assume the samples are simple random samples obtained form populations with normal distributions.

Men: 24.9, 28.4, 23.2, 32.8, 25.3, 32.9, 28.1, 28.6, 32.9, 26.4

Women: 19.6, 23.7, 18.2, 34.5, 19.3, 24.3, 18.8, 33.8, 18.7, 24.1

A. construct a 90% confidence interval estimate of the standard deviation of BMIs for men

_ < σmen < _

B. construct a 99% confidence interval estimate of the standard deviation of BMIs for women

_ < σwomen < _

Answer 1

a)

For men,

= 26.35

S = 8.2386

df = n -1 = 10 - 1 = 9

From Chi-square table,

chi-square critical values at 0.10 significance level with 9 df = L =3.325 ,  U = 16.919

90% confidence interval for is

Sqrt [ ( n -1) S2 / U] < < Sqrt [ ( n -1) S2 / L]

sqrt [ 9 * 8.23862 / 16.919 ] < < sqrt [ 9 * 8.23862 / 3.325 ]

6.01 < < 13.55

b)

For women,

= 23.5

S = 6.0937

df = n -1 = 10 - 1 = 9

From Chi-square table,

chi-square critical values at 0.01significance level with 9 df = L = 1.735 ,  U = 23.589

99% confidence interval for is

Sqrt [ ( n -1) S2 / U] < < Sqrt [ ( n -1) S2 / L]

sqrt [ 9 * 6.09372 / 23.589 ] < < sqrt [ 9 * 6.09372 / 1.735 ]

3.76 < < 13.88