A random sample of 50 business students required an average

A random sample of 50 business students required an average of 43.4 minutes to complete a statistics exam. Assume that the population standard deviation to complete the exam was 8.7 minutes. 1) Compute the standard deviation of the mean for this sample. 2) Compute the margin of error at 95% confidence level for this sample. 3) Compute the confidence interval for the population mean at 95% confidence level.

Solution

Given n=50, sample mean (xbar)=43.4, =8.7.   The standard deviation of the mean for this sample is (n-1)S²=ns²=>s²=74.1762. Standard error(xbar)=/n=8.7/(50)=1.2305. The margin of error at 95% confidence level for this sample is (xbar+-[(1.96)*(/n)]=(40.9882,45.8118). The 95% confidence interval for the population mean is (xbar+-[(1.96)*((s²/n))])=(41.0126,45.7873).