A simple random sample of size n is drawn from a population that is normally distributed. The sample mean,

x,

is found to be

18.9,

and the sample standard deviation, s, is found to be

4.4.

(a) Construct a

98%

confidence interval about

if the sample size, n, is

31.

(b) Construct a

98%

confidence interval about

if the sample size, n, is

67.

How does increasing the sample size affect the margin of error, E?

(c) Construct a

99%

confidence interval about

if the sample size, n, is

31.

How does increasing the level of confidence affect the size of the margin of error, E?

(d) If the sample size is

12,

what conditions must be satisfied to compute the confidence interval?