1. Chapter 5 Hypothesis Tests With Means of Samples
Part 1: Sept. 10, 2013

2. The Distribution of Means
In Ch 4, comparison distributions discussed were distributions of individual scores
Now, interested in mean of a group of scores
Comparison distribution of interest will be distribution of means

3. The Distribution of Means
Consists of means of a very large number of samples of the same size
Each sample randomly taken from the same population of individuals
Each point in distribution is a group mean
This will be your comparison distribution when you have N>1.

4. The Distribution of Means
How is it created? Example…
Population N=100, want sample n=5 test scores
1st random sample = persons 6, 27, 45, 88, 91 (M=78.4)
2nd random sample = persons 18, 30, 56, 59, 79 (M=82.5)
Plot 78.4, 82.5, etc.
Should look approximately normally distributed

5. The Distribution of Means
Characteristics - assuming a large N
Its mean is the same as
the mean of the population
of individuals
Its variance is the variance
of the population divided by
the number of individuals in
each of the samples
Mean of distribution of means
Variance of distribution of means

6. The Distribution of Means
Characteristics
Its standard deviation is the square root of its variance
SD of distribution of means also known as standard error (σM).
( How much the means of samples are ‘in error’ as estimate of mean of the population.)

7. The Distribution of Means
Shape: it is approximately normal if either
Each sample is of 30 or more individuals or
The distribution of the population of individuals is normal
Example…

8. Hypothesis Testing With a Distribution of Means
Distribution of means will be your comparison distribution
1) Find a Z score of your sample’s mean on a distribution of means
Z score formula conceptually same as before, but now refers to means of sample & comparison distrib
Sample mean
Mean of distrib of
means
Std dev of distrib of
means

9. Example
Your sample’s mean is 220 (n=64), distribution of means has mean=200, std dev = 6.

10. Example - #9 from practice prob. (p. 182)
1-sample z test:
Used 1-10 scale to indicate fault of driver in accident.
Population distribution has  = 5.5 and  = .8
Here, 16 students rated fault when asked how likely the driver who crashed into other was at fault?
This sample (n=16) had mean=5.9.
Did the manipulation significantly increase fault results?
that is, compare our sample mean to the pop mean
is 5.9 significantly higher than 5.5?