Question

You randomly select and measure the contents of 10 bottles of cough syrup. The results​ (in fluid​ ounces) are shown to the right.

4.212 4.295 4.255 4.243 4.187 4.268 4.267 4.242 4.228 4.236

Assume the sample is taken from a normally distributed population.

Construct 99​%

confidence intervals for​ (a) the population variance σ^2

and​ (b) the population standard deviation σ.

*PLEASE ROUND TO 6 DECIMAL POINTS*

Answer 1

The statistical software output for this problem is :

One sample variance confidence interval:
σ² : Variance of variable

99% confidence interval results:

Variable	Sample Var.	DF	L. Limit	U. Limit
Data	0.00093556667	9	0.00035694497	0.0048532713

(a)

The 99% confidence interval for ² is,

(0.000357 , 0.004853)

(b)

The 99% confidence interval for is,

(0.018893 , 0.069665)