Answer to Question #178228 in Statistics and Probability for Nimesh Jayamanne

Question #178228

In a random sample of 500 observations drawn from a normal population, the sample mean and sample standard deviation were calculated as X =350 and s = 100.

a) Estimate the population mean with 99% confidence.

b) Repeat part (a) assuming that you know that the population standard deviation is  = 100.

c) Explain why the interval estimates were virtually identical. 


1
Expert's answer
2021-04-15T06:57:36-0400

a) 99% interval estimate of "\\mu" :

"\\overline{x}\\pm z_{\\alpha\/2}s\/\\sqrt{n}=350\\pm 2.586\\cdot100\/\\sqrt{500}="

"=350\\pm 11.564=(338.436,361.564)"


b)

"\\overline{x}\\pm z_{\\alpha\/2}s=350\\pm 2.586\\cdot100=350\\pm 258.6=(91.4,608.6)"


c) The interval estimates were virtually identical because the variable is normally distributed and the sample size is large (more than 30).


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