Question

Find the confidence level associated to the confidence interval extending from 3.64 to 54.25 for the population variance of a Normally distributed random variable X if a sample of 8 observations has a standard deviation of 3.1. Answer?

Answer 1

given data are:-

sample sd (s) = 3.1

sample size (n) = 8

let, we are using c % confidence level, and = (1-c).

the chi square critical value for , df= 7, both tailed test be:-

the c% confidence interval for population variance is:-

according to the problem:-

[ in any blank cell of excel type =CHISQ.DIST(18.480769,7,TRUE)]

the confidence level (c) is = (1-) = (1-0.02) = 0.98 = 98%

the confidence level associated to the confidence interval is = 98%

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