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

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Let x1,...,x20 be a random sample from N(&#956;, &#963;^2) where &#963;^2 s estimated by s^2. If a 90% CI for &#956; is (19.170, 21.138)
a. Obtain a 95% CI for &#963;^2.

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

https://brainmass.com/statistics/chi-squared-test/confidence-intervals-random-sample-chi-square-test-43228

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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 ...

#### Solution Summary

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

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