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.

(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?

Transcribed Image Text:

156 190 147 173 159 181 162 130 101 147 113 109 1.5 0.5 -0.5 82889881 -1 -1.5 Diameter 100 120 1à0 160 180 Diameter 06 70- Expected z-Score