Question

You randomly select and measure the contents of 1010 bottles of cough syrup. The results​ (in fluid​ ounces) are shown to the right.

4.219 4.295 4.251 4.249 4.185 4.298 4.264 4.246 4.224 4.237

Assume the sample is taken from a normally distributed population. Construct 80​%

confidence intervals for​

(a) the population variance

σ^2

and​ (b) the population standard deviation

σ.

*PLEASE ROUND TO 6 DECIMAL PLACES*

Answer 1

The statistical software output for this problem is :

One sample variance confidence interval:
σ² : Variance of variable

80% confidence interval results:

Variable	Sample Var.	DF	L. Limit	U. Limit
Data	0.0011635111	9	0.00071314662	0.0025122842

(a)

The 80% confidence interval for ² is,

(0.000713 , 0.002512)

(b)

The 80% confidence interval for is,

(0.026705 , 0.050123)