(a) Compute the 90% confidence interval estimate of the population variance. A confidence interval for the population variance o? will have the following form where n is the sample size and s? is the sample variance. The x? values correspond to a chi-square distribution with n - 1 degrees of freedom where and 1 - are the upper tail areas. (n – 1)s² x1- a/2 (n – 1)s2 Recall that the value of alpha is found by setting the confidence level equal to (1 – a) and solving for a. A 90% confidence interval is to be found. Expressing 90% as a probability gives 0.90, so we have 1 - a = 0.90. Therefore, a = 0.10, so 4 - ] and 1 - 4 - 2 The sample size is n = 20, so the degrees of freedom is n - 1 =

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(a) Compute the 90% confidence interval estimate of the population variance.
A confidence interval for the population variance a? will have the following form where n is the sample size
and s? is the sample variance. The x? values correspond to a chi-square distribution with n - 1 degrees of
freedom where " and 1 -.
a
are the upper tail areas.
2
(n - 1)s?
2
X al2
(n - 1)s?
2
X1- a/2
Recall that the value of alpha is found by setting the confidence level equal to (1 - a) and solving for a. A
90% confidence interval is to be found. Expressing 90% as a probability gives 0.90, so we have 1 - a = 0.90.
Therefore, a = 0.10, so
2
and 1 -
2
=
The sample size is n = 20, so the degrees of freedom is n - 1 =
Submit
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Transcribed Image Text:(a) Compute the 90% confidence interval estimate of the population variance. A confidence interval for the population variance a? will have the following form where n is the sample size and s? is the sample variance. The x? values correspond to a chi-square distribution with n - 1 degrees of freedom where " and 1 -. a are the upper tail areas. 2 (n - 1)s? 2 X al2 (n - 1)s? 2 X1- a/2 Recall that the value of alpha is found by setting the confidence level equal to (1 - a) and solving for a. A 90% confidence interval is to be found. Expressing 90% as a probability gives 0.90, so we have 1 - a = 0.90. Therefore, a = 0.10, so 2 and 1 - 2 = The sample size is n = 20, so the degrees of freedom is n - 1 = Submit Skip (you cannot come back)
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