Question

You randomly select and measure the contents of 10 bottels of cough syrup. The results in (fluid ounces) are shown in the table below. Assume the sample is taken from a normally distributed population. Construct 80% confidence intervals for (a) the population variance and (b) the population standard deviation. ​(a) The confidence interval for the population variance is: ​(Round to six decimal places as​ needed.) 4.218 4.257 4.182 4.264 4.221 4.298 4.249 4.285 4.249 4.233

** My main question is, can this be done on a Ti-83, or is there a shorter way of finding the answer? I'm doing everything out, it just takes so long! please provide steps to plug into calculator; and where you getting the numbers! thanks!

Answer 1

(a) The confidence interval for population variance:

Step 1:

From the given data, the sample statistics are calculated:

n = sample size = 10

= sample mean = 42.456/10 = 4.2456

s = sample SD = 0.0339

s² = sample variance = 0.001151

= 0.20

Step 2:

Confidence interval for population variance is given by:

Degrees of freedom = n - 1 = 10 - 1 = 9

Low end:

From Table:

High end:

From Table:

Thus,

Confidence interval for population variance is:

0.0007 < < 0.0025

(b) Confidence interval for population SD :

Low end:

High end:

Confidence interval for population SD :

0.0266< < 0.0499