A psychologist wishes to estimate the average reaction time to a stimulus among 200 patients in a hospital specializing in nervous disorders.

A psychologist wishes to estimate the average reaction time to a stimulus among 200 patients in a hospital specializing in nervous disorders. A simple random sample of size n = 20 patients was selected, and their reaction times were measured with the following results; the sample mean, y = 1.2 seconds and sample standard deviation s = 4.0 seconds.i) Estimate the population mean Y and total Y.ii) What is the bound of the error of estimation on each of the estimators in (i)?iii) Construct a 95% confidence interval for Y and for Y.iv) How large a sample should be taken in order to estimate Y with a bound of 1 second on the error of estimation? Use 1.0 second as an approximation of the population standard deviation.