Question

A sample of 25 items provides a sample standard deviation of 6. (a) Compute the 90% confidence interval estimate of the population variance. (Round your answers to two decimal places.) ____ to ____ (b) Compute the 95% confidence interval estimate of the population variance. (Round your answers to two decimal places.) _____to _____ (c) Compute the 95% confidence interval estimate of the population standard deviation. (Round your answers to one decimal place.) _____to ____

Answer 1

Solution :

Given that,

(a)

s = 6

Point estimate = s² = 36

²_R = ²_/2,df = 36.415

²_L = ²_{1 - /2,df} = 13.848

The 90% confidence interval for ² is,

(n - 1)s² / ²_/2 < ² < (n - 1)s² / ²_{1 - /2}

(24)(36) / 36.415 < ² < (24)(36) / 13.848

23.73 < ² < 62.39  

(23.73 to 62.39)

(b)

s = 6

Point estimate = s² = 36

²_R = ²_/2,df = 39.364

²_L = ²_{1 - /2,df} = 12.401

The 95% confidence interval for ² is,

(n - 1)s² / ²_/2 < ² < (n - 1)s² / ²_{1 - /2}

(24)(36) / 39.364 < ² < (24)(36) / 12.401

21.95 < ² < 69.67

(21.95 to 69.67)

(c)

s = 6

s² = 36

²_R = ²_/2,df = 39.364

²_L = ²_{1 - /2,df} = 12.401

The 95% confidence interval for is,

(n - 1)s² / ²_/2 < < (n - 1)s² / ²_{1 - /2}

(24)(36) / 39.364 < < (24)(36) / 12.401

4.7 < < 8.3

(4.7 to 8.3 )