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Use technology to construct the confidence intervals for the population variance sigma squared and the population...

Use technology to construct the confidence intervals for the population variance sigma squared and the population standard deviation sigma. Assume the sample is taken from a normally distributed population. cequals0.98​, ssquaredequals7.84​, nequals28 The confidence interval for the population variance is

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Expert Solution

Solution :

Given that,

c = 0.98

s = 7.84

n = 28

At 98% confidence level the is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

/2,df = 0.01,27 = 23.68

and

1- /2,df = 0.99,27 = 6.57

Point estimate = s2 = 7.84

2L = 2/2,df = 23.68

2R = 21 - /2,df = 6.57

The 98% confidence interval for 2 is,

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

( 27*7.84) / 23.68 < 2 < ( 27 * 7.84) / 6.57

4.51 < 2 < 16.44

(4.51 , 16.44)

orchestra answered 1 year ago
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