Transcript Ch. 11 PowerPoints

Figure 11.1 The law of large numbers in action: as we take more observations, the sample mean ¯
x always
approaches the mean m of the population.
The Basic Practice of Statistics, 6th Edition
David S. Moore, William I. Notz, Michael A. Fligner
Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company
Figure 11.2 The idea of a sampling distribution: take many samples from the same population, collect the ¯
x’s
from all the samples, and display the distribution of the ¯
x’s. The histogram shows the results of 1000 samples.
The Basic Practice of Statistics, 6th Edition
David S. Moore, William I. Notz, Michael A. Fligner
Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company
Figure 11.3 The distribution of single observations (the population distribution) compared with the sampling
distribution of the means ¯
x of 10 observations, for Example 11.5. Both have the same mean, but averages are
less variable than individual observations.
The Basic Practice of Statistics, 6th Edition
David S. Moore, William I. Notz, Michael A. Fligner
Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company
Figure 11.4 The central limit theorem in action, for Example 11.6. (a) The distribution of earned income in a
population of 75,310 households.
The Basic Practice of Statistics, 6th Edition
David S. Moore, William I. Notz, Michael A. Fligner
Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company
Figure 11.4 (Continued)
(b) The distribution of the mean earnings for 500 SRSs of 100 households each from this population.
The Basic Practice of Statistics, 6th Edition
David S. Moore, William I. Notz, Michael A. Fligner
Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company
Figure 11.4 (Continued)
(c) The distribution of the sample means in more detail: the shape is close to Normal.
The Basic Practice of Statistics, 6th Edition
David S. Moore, William I. Notz, Michael A. Fligner
Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company
Figure 11.5 The central limit theorem in action, for Example 11.7. The distribution of sample means ¯
x from a
strongly non-Normal population becomes more Normal as the sample size increases. (a) The distribution of 1
observation. (b) The distribution of ¯x for 2 observations. (c) The distribution of x for 10 observations. (d) The
distribution of ¯
x for 25 observations.
The Basic Practice of Statistics, 6th Edition
David S. Moore, William I. Notz, Michael A. Fligner
Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company
Figure 11.6 The exact distribution (dotted) and the Normal approximation from the central limit theorem
(solid) for the average time needed to maintain an air conditioner, for Example 11.8. The probability we want is
the area to the right of 1.1.
The Basic Practice of Statistics, 6th Edition
David S. Moore, William I. Notz, Michael A. Fligner
Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company