A master's thesis by M. Purser at the University of Washington in 1988 looked at soil density in a conifer forest. Bulk densities (in grams per cubic cm) for 33 samples were reported in the Quantitative Environmental Learning Project (QELP) posted on www.seattlecentral.org. Their mean was 0.37 and standard deviation was 0.27.

a. Use the fact that the t multiplier for 32 degrees of freedom and 99% confidence is 2.74 to report a 99% confidence interval for the mean density of all soil samples in the forest, rounding to the nearest hundredth.

b. Report a 99% confidence interval for the mean density of all soil samples in the forest, rounding to the nearest hundredth, if the z multiplier is used instead of t.

c. Characterize your intervals in parts (a) and (b) as being very different, slightly different, or identical.

d. Tell whether use of z instead of t multipliers for samples of size 33 makes a big difference, a slight difference, or no difference when constructing confidence intervals.