Let the following sample of 8 observations be drawn from a normal population with unknown mean…

Let the following sample of 8 observations be drawn from a
normal population with unknown mean and standard deviation: 21, 20,
25, 18, 28, 19, 13, 22. [You may find it useful to reference the t
table.]
a. Calculate the sample mean and the sample standard deviation.
(Round intermediate calculations to at least 4 decimal places.
Round “Sample mean” to 3 decimal places and “Sample standard
deviation” to 2 decimal places.)
b. Construct the 90% confidence interval for the population
mean. (Round “t” value to 3 decimal places and final answers to 2
decimal places.)
c. Construct the 99% confidence interval for the population
mean. (Round “t” value to 3 decimal places and final answers to 2
decimal places.)
d. What happens to the margin of error as the confidence level
increases from 90% to 99%? As the confidence level increases, the
margin of error becomes larger. As the confidence level increases,
the margin of error becomes smaller.