Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

A sample of 81 observations is taken from a normal population with a standard de

ID: 3081781 • Letter: A

Question

A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95 percent confidence interval for the population mean. (Round your answers to 3 decimal places.) Confidence interval for the population mean is and .

Explanation / Answer

z = 1.96 (from table lookup) Since n >30, we assume a normal distribution and the sample standard deviation can be substituted for the population standard deviation. The confidence interval is : = xbar ± z * (s / sqrt(n)) = 40 ± 1.96 * (5 / sqrt(81)) = 40 ± 1.96 * (5 / 9) = 40 ± 1.089 = 38.911 to 41.089