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 μ

b. Construct a 95% confidence interval for the population mean μ

c. Construct a 99% confidence interval for the population mean μ

d. Assume that the sample mean x¯ and sample standard deviation s remain exactly the same as those you just calculated, but that they 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?