A random sample of 8 observations was drawn from a normal population. The sample mean and sample standard deviation are x = 40 and s = 10. a. Estimate the population mean with 95% confidence. b....

A random sample of 8 observations was drawn from a normal population. The sample mean and sample standard deviation are x = 40 and s = 10.

a. Estimate the population mean with 95% confidence.

b. Repeat part (a) assuming that you know that the population standard deviation is σ = 10.

c. Explain why the interval estimate produced in part (b) is narrower than that in part (a).