A simple random sample of size n is drawn from a population that is normally distributed....

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A simple random sample of size n is drawn from a population thatis normally distributed. The sampleâ€‹ mean, x overbarâ€‹, is found tobe 112â€‹, and the sample standardâ€‹ deviation, s, is found to be 10.â€‹(a) Construct a 95â€‹% confidence interval about mu if the sampleâ€‹size, n, is 23. â€‹(b) Construct a 95â€‹% confidence interval about muif the sampleâ€‹ size, n, is 16. â€‹(c) Construct a 90â€‹% confidenceinterval about mu if the sampleâ€‹ size, n, is 23. â€‹(d) Could we havecomputed the confidence intervals in partsâ€‹ (a)-(c) if thepopulation had not been normallyâ€‹ distributed?

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Given the random samples are drawn from a normal distributionand also we have sample mean and sample standard deviation Let denote the population meanWe know that the statisticfollows students t distribution with n1 degrees of freedom equation1Hence the confidence limits for are See Answer

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