Question

In: Statistics and Probability

Use technology to construct the confidence intervals for the proportion variance sigma2 and the population standard...

Use technology to construct the confidence intervals for the proportion variance sigma2 and the population standard deviation sigma. Assume the sample is taken from a normally distributed population.

c=0.90, s2=10.89, n=25

The confidence interval for the population variance is (?,?)

The confidence interval for the population standard deviation is (?,?)

Solutions

Expert Solution

Solution :

Given that,

Point estimate = s2 = 10.89

n = 25

Degrees of freedom = df = n - 1 = 24

2L = 2/2,df = 36.415

2R = 21 - /2,df = 13.848

The 90% confidence interval for 2 is,

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

24 * 10.89 / 36.415 < 2 < 24 * 10.89 / 13.848

7.18 < 2 < 18.87

The 90% confidence interval for 2 is, (7.18 , 18.87) .

The confidence interval for the population standard deviation is,

2.68 < < 4.34


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