Chi-Square Tests &
Final Exam Review
Chapter 12
Cathy Poliak, Ph.D.
Office Fleming 11c
Department of Mathematics
University of Houston
Lecture 14 - 3339
Cathy Poliak, Ph.D. Office Fleming 11c (Department
Chapter 12 of Mathematics University of Houston
Lecture) 14 - 3339
, Outline
1 Goodness of Fit Tests
2 Chi-Square
3 Examples
4 χ2 Test of Independence
5 Final Exam Review
6 Examples
Cathy Poliak, Ph.D. Office Fleming 11c (Department
Chapter 12 of Mathematics University of Houston
Lecture) 14 - 3339
, Candy
Mars Inc. claims that they produce M&Ms with the following
distributions:
Brown 30% Red 20% Yellow 20%
Orange 10% Green 10% Blue 10%
A bag of M&Ms was randomly selected from the grocery store shelf,
and the color counts were:
Brown 14 Red 14 Yellow 5
Orange 7 Green 6 Blue 10
We want to know if the distribution of color the same as the
manufacturer’s claim.
Cathy Poliak, Ph.D. Office Fleming 11c (Department
Chapter 12 of Mathematics University of Houston
Lecture) 14 - 3339
, Goodness-of-fit Test
This is a test to see how well on sample proportions of categories
"match-up" with the known population proportions.
The Chi-square goodness-of-fit test extends inference on
proportions to more than two proportions by enabling us to
determine if a particular population distribution has changed from
a specified form.
Hypotheses:
I H0 : The proportions are the same as what is claimed.
I Ha : At least one proportion is different as what is claimed.
This would be better in context of the problem. For example in our
M&Ms test;
I H0 : The distribution of candy colors is as the manufacturer claims.
I Ha : The distribution of candy colors is not what the manufacturer
claims.
Cathy Poliak, Ph.D. Office Fleming 11c (Department
Chapter 12 of Mathematics University of Houston
Lecture) 14 - 3339
Final Exam Review
Chapter 12
Cathy Poliak, Ph.D.
Office Fleming 11c
Department of Mathematics
University of Houston
Lecture 14 - 3339
Cathy Poliak, Ph.D. Office Fleming 11c (Department
Chapter 12 of Mathematics University of Houston
Lecture) 14 - 3339
, Outline
1 Goodness of Fit Tests
2 Chi-Square
3 Examples
4 χ2 Test of Independence
5 Final Exam Review
6 Examples
Cathy Poliak, Ph.D. Office Fleming 11c (Department
Chapter 12 of Mathematics University of Houston
Lecture) 14 - 3339
, Candy
Mars Inc. claims that they produce M&Ms with the following
distributions:
Brown 30% Red 20% Yellow 20%
Orange 10% Green 10% Blue 10%
A bag of M&Ms was randomly selected from the grocery store shelf,
and the color counts were:
Brown 14 Red 14 Yellow 5
Orange 7 Green 6 Blue 10
We want to know if the distribution of color the same as the
manufacturer’s claim.
Cathy Poliak, Ph.D. Office Fleming 11c (Department
Chapter 12 of Mathematics University of Houston
Lecture) 14 - 3339
, Goodness-of-fit Test
This is a test to see how well on sample proportions of categories
"match-up" with the known population proportions.
The Chi-square goodness-of-fit test extends inference on
proportions to more than two proportions by enabling us to
determine if a particular population distribution has changed from
a specified form.
Hypotheses:
I H0 : The proportions are the same as what is claimed.
I Ha : At least one proportion is different as what is claimed.
This would be better in context of the problem. For example in our
M&Ms test;
I H0 : The distribution of candy colors is as the manufacturer claims.
I Ha : The distribution of candy colors is not what the manufacturer
claims.
Cathy Poliak, Ph.D. Office Fleming 11c (Department
Chapter 12 of Mathematics University of Houston
Lecture) 14 - 3339
