Question

A magazine includes a report on the energy costs per year for 32-inch liquid crystal display (LCD) televisions. The article states that 14 randomly selected 32-inch LCD televisions have a sample standard deviation of $3.59. Assume the sample is taken from a normally distributed population. Construct 98% confidence intervals for (a) the population variance σ2 and (b) the population standard deviation σ. Interpret the results. (a) The confidence interval for the population (b) (Round to two decimal places as needed.)

Answer 1

Solution:

Given:

n = sample size = 14

s = Sample Standard Deviation = 3.59

We have to construct 98% confidence intervals for

Part a) the population variance σ² :

where

and are chi-square critical values.

df = n - 1 = 14 - 1 = 13

c = 98% = 0.98

then 1 - c= 1 - 0.98 = 0.02

Find: and

Look in Chi-square table for df = 13 and right tail area 0.01 and 0.99 and find corresponding critical values.

Thus

= 27.688

= 4.107

Thus

Part b) The population standard deviation σ.