For the data of Problem 6: a. Find the mean, median, and 10% and 20% trimmed means....

For the data of Problem 6:

a. Find the mean, median, and 10% and 20% trimmed means.

b. Find an approximate 90% confidence interval for the mean.

c. Find a confidence interval with coverage near 90% for the median.

d. Use the bootstrap to find approximate standard errors of the trimmed means.

e. Use the bootstrap to find approximate90%confidence intervals for the trimmed means.

f. Find and compare the standard deviation of the measurements, the interquartile range, and the MAD.

g. Use the bootstrap to find the approximate sampling distribution and standard error of the upper quartile.

Reference

Various chemical tests were conducted on beeswax by White, Riethof, and Kushnir (1960). In particular, the percentage of hydrocarbons in each sample of wax was determined.

a. Plot the ecdf, a histogram, and a normal probability plot of the percentages of hydrocarbons given in the following table. Find the .90, .75, .50, .25, and .10 quantiles. Does the distribution appear Gaussian?

b. The average percentage of hydrocarbons in microcrystalline wax (a synthetic commercial wax) is 85%. Suppose that beeswax was diluted with 1% micro- crystalline wax. Could this be detected? What about a 3% or a 5% dilution? (Such questions were one of the main concerns of the beeswax study.)