Question

You randomly select and measure the contents of 10 bottles of cough syrup. The results​ (in fluid​ ounces) are shown to the right. 4.218 4.299 4.255 4.248 4.184 4.296 4.265 4.246 4.228 4.232 Assume the sample is taken from a normally distributed population. Construct 95​% confidence intervals for​ (a) the population variance sigma squared and​ (b) the population standard deviation sigma. Interpret the results.

Answer 1

From sample data,

= 4.24 , S = 0.0314

a)

Chi-square critical values at 0.05 significance level with 8 df = 1.690 , 16.013

95% confidence interval for is

( n - 1) S² / U < < ( n - 1) S² / L

8 * 0.03142² / 16.013 < < 8 * 0.03142² / 1.690

0.0005 < < 0.0047

95% CI Is ( 0.0005 , 0.0047 )

b)

95% confidence interval for is

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

sqrt [ 8 * 0.03142 / 16.013] < < sqrt [ 8 * 0.03142 / 1.690 ]  

0.0224 < < 0.0686

95% CI Is ( 0.0224 , 0.0686 )