Question

A researcher collected data on an attitude scale which had a µ of 10 and a population standard deviation of 6. (a) With a random sample of 20, he wants to know what the standard error of the mean would be. (b) Calculate the 95% confidence interval (using z) for the example above for a sample mean of 8.

Answer 1

So, standard error is 6/sqrt(5) or 1.3416 (approx)

b) For 95% CI z = 1.96

When we calculate confidence interval (CI) then we use sample mean which is 8 given in part b)

CI = (8 - 2.63, 8 + 2.63)

CI = (5.37, 10.63)

So, we are 95% confident that the true population mean lies between 5.37 and 10.63.

Please comment if any doubt. Thank you.