A random sample of n = 12 four-year-old red pine trees was selected, and the diameter (i...

A random sample of n = 12 four-year-old red pine trees was selected, and the diameter (in inches) of each tree’s main stem was measured. The resulting observations are as follows:

a. Compute a point estimate of σ, the population standard deviation of main stem diameter. What statistic did you use to obtain your estimate?

b. Making no assumptions about the shape of the population distribution of diameters, give a point estimate for the population median diameter. What statistic did you use to obtain the estimate?

c. Suppose that the population distribution of diameter is symmetric but with heavier tails than the normal distribution. Give a point estimate of the population mean diameter based on a statistic that gives some protection against the presence of outliers in the sample. What statistic did you use?

d. Suppose that the diameter distribution is normal. Then the 90th percentile of the diameter distribution is μ+ 1.28σ (so 90% of all trees have diameters less than this value). Compute a point estimate for this percentile. (Hint: First compute an estimate of σ in this case; then use it along with your estimate of s from Part (a).)