Chapter 8.2, Problem 19P

19

Critical Thinking: Boxplots and Confidence Intervals The distribution of heights of 18-year-old men in the United States is approximately normal. with mean 68 inches and standard deviation 3 inches (U.S. Census Bureau). In Minitab, we can simulate the drawing of random samples of size 20 from this population (► Cale ► Random Data ► Normal, with 20 rows from a distribution with a mean of 68 and a standard deviation of 3). Then we can have Minitab compute a 95% confidence interval and draw a boxplot of the (► Stat ► Basic Statistics ► 1—Sample t, with boxplot selected in the graphs). The boxplots and confidence intervals for four different samples are shown in the accompanying figures. The four confidence intervals are

VARIABLE	N	MEAN	STDEV	SEMEAN	95.0	% CI
Sample 1	20	68.050	2.901	0.649		69.407)
Sample a	20	67.956	3.137	0.702	(66.490	69.426
Sample 3	20	67.976	2.639	0.590	(66.741 ,	69.211)
Sample 4	20	66.908	2.440	0.546	(65.766 ,	68.050)

(a) Examine the figure (parts (a) to (d)). How do the boxplots for the four samples differ? Why should you expect the boxplots to differ ?

(b) Examine the 95% confidence intervals for the four sample shown in the printout. Do the intervals differ in length? Do the intervals all contain the expected population mean of tot inches? If we draw more samples, do you expect all of the resulting 95% confidence intervals to contain µ = 68 ? Why or why not?