Question

In: Statistics and Probability

A magazine includes a report on the energy costs per year for​ 32-inch liquid crystal display​...

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 ​$3.37. 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.

Solutions

Expert Solution

Solution :

Given that,

s = 3.37

Point estimate = s2 = 11.3569

2R = 2/2,df = 24.736

2L = 21 - /2,df = 5.009

The 95% confidence interval for 2 is,

(n - 1)s2 / 2/2 < 2 < (n - 1)s2 / 21 - /2

13 * 11.3569 / 24.736 < 2 < 13 * 11.3569 / 5.009

5.9687 < 2 < 29.4767

(5.9687 , 29.4767)

(b)

The 95% confidence interval for is,

2.4431 < < 5.4292

(2.4431 , 5.4292)


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