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CHAPTER 5: Statistics Topics Overview
p. 174 Mean & Standard Deviation
Calculate standard deviation (Sx) by hand (FORMULA)
Questions: p. 176-177 #1-4
p.181-182 Normal Distribution
Questions: p.182-184 #12-17
p.187-188 Sampling Methods
Questions: p.189-190 #1-5
p.196-197 Central Limit Theorem
Questions: p.198-199 #4-9
Confidence Intervals
p.202-204
Confidence Intervals when population mean and standard deviation given
Questions: p.205 #20
p.209-210
Confidence Intervals when population mean and standard deviation NOT given
Questions: p.211 #28-30
Statistics Unit Detailed Summary
For more complete summary, see unit summary p.234-239
Population – the set representing all measurements of interest to the investigator
Sample – a subset of measurements selected from a population of interest
Topics
1. Calculating Standard Deviations (Formulae p.174 & 176, Exercises1-4 pp.176-178)
2. Simulations (p.179-180)** (**We may not cover)
3. Normal Distribution (p.181-182, Exercises #12-17 p.182-184)
4. Sampling Methods (p.187-188, Exercises #1-5 p.189-190, p.244#4)
Symbols


x
Sx
Population Mean
Population Standard Deviation
Sample Mean
Sample Standard Deviation
x
Mean of Sample Means
x
Standard Deviation of Sample Means
5.
Sampling Distribution of Sample Mean (Central Limit Theorem)
Values of the sample mean are unpredictable and vary from sample to sample. To make predictions about a
population, we must repeatedly draw random samples of a specific size from a population. If the mean of each
sample has been taken, the mean of these sample means would be approximately equal to the population mean.
x = 
(  is the symbol for ‘mean of sample means’)
x
Also, the following equation represents the standard deviation of all the sample means (x)
x=

n
(  is the standard deviation of all the sample means found,  is the population standard
x
deviation & n in the size of the samples drawn)
See Example 1 p.197, Try Exercises #3-8 p.198-199
6.
Point Estimates and Confidence Intervals
A simple sample mean is called a point estimate because this single number can be used as a possible estimate of the
population mean. Because this is often inaccurate, we instead find an interval in which we are confident that that the
population mean would be contained. This is a confidence interval.
Confidence Intervals
Earlier in the unit we approximated that 95% of the data falls within 2 standard deviations of the mean. In fact, 95%
of the data actually falls within 1.96 standard deviations of the mean.
Depending on the “percent confidence” you are looking for, you will use different z-values (i.e.1.96) to represent the
number of standard deviations from the mean.
_
Confidence Interval Formulae  x
_
 z _
or
x  z
x

n
Z-value chart 
Confidence Interval
90%
95%
99%
z-value
1.645
1.96
2.56
Example:
Joe collects a sample of size 35 from a known population with a population mean of 250 and a population standard
deviation of 20. She finds that the sample mean is 246.
Determine the 95% confidence interval for this sample.
_
x  z

246
n
 1.96
95% Confidence Interval 
20
246
35
 6.6
239.4 to 252.6
Description of Answer: The mean will be between 239.4 and 252.6 95% of the time.
(19 times out of 20)
(see pp.201-205, Exercises #20,21 pp.205-206)
Confidence Intervals When  is Unknown
_
We used x
 z

to calculate confidence intervals.
n
It is most likely, however, that you WON’T know the population standard deviation () when calculating
confidence intervals for real-life sample data. Instead, we will simply use the sample standard deviation (Sx) in
place of , so long as the sample size is large enough (n30).
The following formula will be used as our interval estimator:
_
Confidence Interval Formula for Samples 
Note: The z
Sx
n
x  z
Sx
n
part of the formula is called the margin of error.