Download Q9.R.14 Estimating a Population Mean

Estimating a Population Mean
We selected Q9.R.14 (p.425) as an example of using StatCrunch to find a confidence interval for  .
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.
(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. 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.
(a) Obtain a point estimate for the mean and standard deviation diameter of a Douglas fir tree in the western
Washington Cascades.
The best point estimate for the population mean is the sample mean, x .
The best point estimate for the population variance is the sample variance, s 2 .
We are going to use StatCrunch to find x and s .
Step 1: Download the data set.
(Note: Due to a StatCrunch mistake, the data set is obtained from 9_r_15.txt, not from 9_r_14_txt.)
Step 2: Click Stat → Summary Stats → Columns.
Step 3: 1) Choose Diameter of Douglas fir Tree under Select column(s):
2) Under Statistics:, choose Mean and Std. dev.
(Choose each item while holding the Ctrl key on the keyboard)
3) Click Compute!
Step 4: The point estimate of mean and standard deviation are obtained.
The point estimate of mean is x  147.33333  147.3 cm.
The point estimate of standard deviation is s  28.817082  28.8 cm.
(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. Are the conditions for constructing a confidence interval for the population mean diameter
satisfied?
The normal probability plot is roughly linear and the data do not contain outliners in the boxplot.
Therefore, the conditions are met so t  interval procedures can be used.
(c) Construct a 95% confidence interval for the mean diameter of a Douglas fir tree in the western Washington
Cascades.
Step 1: Back in StatCrunch data, click Stat → T Stats → One Sample → With Data.
Step 2: 1) Choose Diameter of Douglas Fir Tree under Select column(s):
2) Under Perform: --> click Confidence interval for  , and type 0.95 for Level:.
3) Click Compute!
The 95% confidence interval for the mean diameter is computed and shown below.
Lower bound = 129.02383  129.0 and Upper bound = 165.64283  165.6.
We are 95% confident that the population mean diameter of a Douglas fir tree in the western Washington
Cascades is between 129.0 cm and 165.6 cm.