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

Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbarx, is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct a 96% confidence interval about if the sample size, n, is 27. (b) Construct a 96% confidence interval about if the sample size, n, is 23. (c) Construct a 70% confidence interval about if the sample size, n, is 27. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?

Explanation / Answer

a) here std error =std deviation/(n)1/2 =1.9245

and for 96% CI and n-1=26 degree of freedom; t=2.162

hence confidence interval =mean +/- t*std error =105.8392 ; 114.1608

b)

here std error =std deviation/(n)1/2 =2.085

and for 96% CI and n-1=22 degree of freedom; t=2.1829

hence confidence interval =mean +/- t*std error =105.4484 ; 114.5516

c)

here std error =std deviation/(n)1/2 =1.9245

and for 70% CI and n-1=26 degree of freedom; t=1.0575

hence confidence interval =mean +/- t*std error =107.9648 ; 112.0352

d)

Yes, as we have used t dstribution which gives a wider confidence interval for comensate for that.

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