?Diameter of Douglas Fir Trees The diameter of the Douglas fir tree is measured at a height of 1.37 meters. The following data represent the diameter i

Chapter 9, Problem 15

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Diameter of Douglas Fir Trees The diameter of the Douglas fir tree is measured at a height of 1.37 meters. The following data represent the diameter in centimeters of a random sample of 12 Douglas firs in the western Washington Cascades.

Source: L. Winter. “Live Tree and Tree-Ring Records to Reconstruct the Structural Development of an Old-Growth Douglas Fir/Western Hemlock Stand in the Western Washington Cascades.” Corvallis, OR: Forest Science Data Bank, 2005.

(a) Obtain a point estimate for the mean and standard deviation diameter of a Douglas fir tree in the western Washington Cascades.

(b) Because the sample size is small, we must verify that the data come from a population that is normally distributed and that the data do not contain any outliers. The figures show

the normal probability plot and boxplot. The correlation between the tree diameters and expected z-scores is 0.982. Are the conditions for constructing a confidence interval for the population mean diameter satisfied?

(c) Construct a 95% confidence interval for the mean diameter of a Douglas fir tree in the western Washington Cascades.

(d) Construct a 95% confidence interval for the standard deviation diameter of a Douglas fir tree in the western Washington Cascades.