Question: The following random sample was selected from a normal distribution: 4, 6, 3, 5, 9, 3.

(a) Construct a 90% confidence interval for the population mean \(\mu \).

(b) Construct a 95% confidence interval for the population mean \(\mu \).

(c) Construct a 99% confidence interval for the population mean p..

(d) Assume that the sample mean \(\bar{X}\) and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n = 25 observations rather than n = 6 observations. Repeat parts a–c. What is the effect of increasing the sample size on the width of the confidence intervals?