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In: Statistics and Probability

construct the indicated confidence intervals for the population variance and the poplulation standard deviation. assume the...

construct the indicated confidence intervals for the population variance and the poplulation standard deviation. assume the sample is from a normally distributed population. c=0.95, s2=15.40, n=25

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Expert Solution

Solution :

Given that,

Point estimate = s2 = 15.40

n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 95% confidence level the 2 value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

2L = 2/2,df = 39.364

2R = 21 - /2,df = 12.401

The 95% confidence interval for 2 is,

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

(24) (15.40) / 39.364 < 2 < (24)(15.40) / 12.401

9.39 < 2 < 29.80

(9.39 , 29.80)

s2 = 15.40

n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 95% confidence level the 2 value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

2L = 2/2,df = 39.364

2R = 21 - /2,df = 12.401

The 95% confidence interval for is,

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

(24)(15.40) / 39.364 < < (24)(15.40) / 12.401

3.06 < < 5.46

(3.06 , 5.46)

orchestra answered 1 year ago
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