Question

Construct the confidence interval for the population standard deviation for the given values. Round your answers to one decimal place.

n=20n=20, s=4.3s=4.3, and c=0.99

Answer 1

Confidence interval for population standard deviation is given as below:

Sqrt[(n – 1)*S2 / χ2 α/2, n – 1 ] < σ < sqrt[(n – 1)*S2 / χ2 1 - α/2, n – 1 ]

We are given

Confidence level = 99%

Sample size = n = 20

Degrees of freedom = n – 1 = 19

Sample standard deviation = S = 4.3

χ2 α/2, n – 1 = 51.3313

χ2 1 - α/2, n – 1 = 9.1055

(By using chi square table)

Sqrt[(n – 1)*S2 / χ2 α/2, n – 1 ] < σ < sqrt[(n – 1)*S2 / χ2 1 - α/2, n – 1 ]

Sqrt[(20 – 1)*4.3^2 / 51.3313] < σ < sqrt[(20 – 1)*4.3^2 / 9.1055]

3.0175 < σ < 7.1646

Lower limit = 3.0

Upper limit = 7.2