A simple random sample of size $n$ is drawn from a population that is normally distributed. The sample mean, $\bar{x}$, is found to be 18.9, and the sample standard deviation, $s$, is found to be 5.9.
(a) Construct a 98% confidence interval about $\mu$ if the sample size, $n$, is 33.
(b) Construct a 98% confidence interval about $\mu$ if the sample size, $n$, is 60. How does increasing the sample size affect the margin of error, $E$?
(c) Construct a 99% confidence interval about $\mu$ if the sample size, $n$, is 33. How does increasing the level of confidence affect the size of the margin of error, $E$?
(d) If the sample size is 23, what conditions must be satisfied to compute the confidence interval?
