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HW-pg. 596 (9.32 - 9.34)
Ch. 9 Test FRIDAY 1-24-14
www.westex.org HS, Teacher Website
1-21-14
Warm up—AP Stats
None!
Name _________________________
AP Stats
9 Sampling Distributions
9.3 Sample Means
Date _______
Objectives
 Given the mean and standard deviation of a population, calculate the mean and standard
deviation for the sampling distribution of a sample mean.
 Identify the shape of the sampling distribution of a sample mean drawn from a
population that has a Normal distribution.
Recap
Sample proportions come up when we are looking at _______________ variables. What
proportion of U.S. adults have watched Survivor? What proportion of U.S. adults believe in
God?
Sample Means
When we record _______________ variables such as income of a household, heart rate of a
person, score on the math section of the SAT, we are interested in other statistics such as the
median or _______ or ________________ _______________ of the variable.
9.3 describes the sampling distribution of the _______ of the responses in an _____.
Looking at the histogram above tells us that:
 Means of random samples are _____ variable than individual observations.
A more detailed examination of the distributions would point to a second principle:
 Means of random samples are _______ Normal than individual observations.
For these 2 reasons sample means are popular in statistical inference.
The Mean and the Standard Deviation of ___.
The sampling distribution of ___ is the distribution of the values of ___ in all possible samples
of the same size from the population. The first histogram above shows the distribution of a
_______________, with mean µ = -3.5% while the second histogram shows the distribution of
the __________ _______ ___ from all samples of size n = 5 from the population. The mean
of all the values of ___ is _______, but the values of ___ are less spread out than the
individual values in the ________________.
Mean and Standard Deviation of a Sample Mean
Suppose that ___ is the mean of an ___ of size __ drawn from a _______ population with
mean µ and standard deviation σ. Then the mean of the sampling distribution of ___ is ___ = µ
and its standard deviation is ___ =
.
The behavior of ___ in repeated samples is similar to the sample proportion ___:
 The sample mean ___ is an unbiased estimator of the population mean µ.

 The values of ___ are _____ spread out for larger samples. Their standard deviation
decreases at the rate ___, so you must take a sample 4 times as large to cut the sd of __
in _______.
 You should use __________ for the sd of ___ only when the population is at least ___
times as large as the sample. (almost always the case)
***These facts about the mean and sd of ___ are true no matter what the _______________
_______________ looks like.*** (More to come about this tomorrow, how exciting!!!)
Example 9.10
The heights of young women varies approximately according to the N(64.5, 2.5) distribution. If
we choose 1 woman at random, the heights we get in repeated choices follow this distribution.
***The distribution of the population is also the distribution of ONE observation chosen at
random.*** Now measure the height of an SRS of 10 young women. The sampling distribution
of their sample mean height ___ will have mean ___ = ___ = 64.5 inches and sd
This just reminds us that the heights of individual women vary widely about the population
mean, whereas the average height of a sample of 10 women is _____ variable.
Sampling Distribution of a Sample Mean from a Normal Population
Draw an SRS of size n from a population that has the Normal distribution with mean µ and sd σ.
Then the sample mean ___ has the Normal distribution with mean µ and sd
. **Tomorrow
we will consider the shape of the sampling distribution of ___ if the shape of the population is
unknown or known to be non-Normal.**
Example 9.11
a) What is the probability that a randomly selected young woman is taller than 66.5 inches?
b) What is the probability that the mean height of an SRS of 10 young women is greater than
66.5 inches?