# Confidence Intervals for a Random Sample : Chi-Square Test

Let x1,...,x20 be a random sample from N(μ, σ^2) where σ^2 s estimated by s^2. If a 90% CI for μ is (19.170, 21.138)

a. Obtain a 95% CI for σ^2.

b. Obtain a 95% prediction interval for a new single observation.

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a) for the sample, N = 20 and df = 19

then the two tailed 90% t value with df 19 is t = 1.729

the mean = (19.170 + 21.138) / 2 = 20.154

then standard error is

SE = (21.138 - 20.154) /1.729 = 0.569

So the sample variance is S squared = n*SE^2 = 20*0.569^2 = 6.475

Use the X2 ...

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Confidence Intervals for a Random Sample are investigated. The solution is detailed and well presented.

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