Variability, Z Scores,
and Normal
Distributions
Announcements
Team Task 1 on Wednesday
Please
sit with your team
No class Monday
Quiz 2 will be Wednesday 1/21
HW1 will be due Wednesday 1/21
Outline
Q
A public school superintendent in Illinois wants to try a new Positive Behavioral Intervention
(PBI) to see if using the program will change the districts student behavior rating. The district
starts
Key
a. Standard error = about 17.73
b.
H 0 : m =500
H1 : m 500
Note: Change 500 to 480 for this problem.
c.
= .0 2 5
= .0 2 5
.125 pt
-z(.025)
0
z(.025)
.125 pt
Z(.025) =1.96
Rejection Region: Reject
Practice Problems: Key
Q1. Suppose that the average dog can understand 165 words; furthermore, the number of
words dogs know is approximately normally distributed and has a standard deviation of 50
wo
Select Quiz Questions
Quiz 1
1. The range is not a particularly useful measure of variability because it ignores so much of the
data.
2. The mode is the most frequently occurring score in a distributi
Sampling Distributions,
Logic of Hypothesis Testing,
& Introduction to Z
Tests
Announcements
Team Task 2 will be Monday
Next Wednesday
Quiz
3
HW 3 Due
Its not that far away!
Midterm:
Monday, Feb. 9
Using Z Scores
Front of Room
1
7
2
3
4
5
6
8
14
9
10
11
12
13
15
16
17
18
19
20
Announcements
No class Monday
Quiz 2 will be Wednesday 1/21
HW1 will be due Wednesday 1/21 and can
be found at the end o
Practice Problems:
Q1. Suppose that the average dog can understand 165 words; furthermore, the number of
words dogs know is approximately normally distributed and has a standard deviation of 50
words.
Sum.
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55 0E: 3 3 2: 83.2 z.
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Team Application Exercise #1
1. You take a random sample of 4 NU students and ask them to report
the number of alcoholic beverages they consumed per week on
average in the past six months. Their score
Independent t-tests
2/13/12
Homework 4 due Wednesday 2/20 (version 1)
Degrees of freedom
o Help us to make an unbiased estimate of a population parameter
o Samples typically less variable than populat
Single Sample t-test
2/11/13
Sample mean is expected to approximate the population mean
The standard error provides a measure of how well a sample mean approximates population
mean
To quantify our
Power
Actual but unknown state of nature
Decision
Fail to
reject H0
Reject
H0
H0 true
(no effect)
Correct
decision
Probability
= 1-
Type I error
Probability
=
H0 false
(effect exists)
Type II error
Pr
Descriptive vs. Inferential Techniques
Descriptive statistical procedures = used to organize and summarize the measurements in
samples and populations. Ways of ordering and grouping data into distribu
Effect Size
2/1/13
d = (M- mu0)/sigma
Larger effect sizes give you more power
Cant change effect size
Delta = d sqrt(n)
Use with Table B
Once you have delta, go to table and find what your power