16.6 Assessing another bootstrap distribution. Refer to the data in Check-in question 16.1 (page 16-6).

FIGURE 16.7 gives a histogram and a Normal quantile plot of 3000 resample means (labeled t*). What do these plots tell you about the sampling distribution of x¯ when n=6 ?

FIGURE 16.7 R graphical output for the Facebook viewing time bootstrap, Exercise 16.6.

Description The output shows a histogram of t that plots density on the vertical axis, ranging from 0.000 to 0.030 in increments of 0.005, versus t asterisk on the horizontal axis, ranging from 2 to 12 with class sizes of approximately 0.35. The distribution if roughly normal between 2.5 and 11.5 with a mean of approximately 7.5. To the right is a normal quantile plot that plots t asterisk on the vertical axis, ranging from 2 to 14 in increments of 2, versus quantiles of standard normal on the horizontal axis, ranging from negative 4 to 4 in increments of 1. Hundreds of points are plotted in a nearly straight linear cluster that rises from left to right. A regression line rises through the center of the cluster from (negative 3, 2) to (3, 12). Nearly all of the points are on the line.