<< Chapter < Page Chapter >> Page >
This module describes how the chi-square distribution is used to conduct goodness-of-fit test.

In this type of hypothesis test, you determine whether the data "fit" a particular distribution or not. For example, you may suspect your unknown data fit a binomialdistribution. You use a chi-square test (meaning the distribution for the hypothesis test is chi-square) to determine if there is a fit or not. The null and the alternate hypotheses for this test may be written in sentences or may be stated as equations orinequalities.

The test statistic for a goodness-of-fit test is:

Σ k ( O E ) 2 E

where:

  • O = observed values (data)
  • E = expected values (from theory)
  • k = the number of different data cells or categories

The observed values are the data values and the expected values are the values you would expect to get if the null hypothesis were true. There are n terms of the form ( O E ) 2 E .

The degrees of freedom are df = (number of categories - 1) .

The goodness-of-fit test is almost always right tailed. If the observed values and the corresponding expected values are not close to each other, then the test statisticcan get very large and will be way out in the right tail of the chi-square curve.

The expected value for each cell needs to be at least 5 in order to use this test.

Absenteeism of college students from math classes is a major concern to math instructors because missing class appears to increase the drop rate. Suppose that a study was done to determine if the actual student absenteeism follows faculty perception. The faculty expected that a group of 100 students would miss class according to the following chart.

Number absences per term Expected number of students
0 - 2 50
3 - 5 30
6 - 8 12
9 - 11 6
12+ 2

A random survey across all mathematics courses was then done to determine the actual number (observed) of absences in a course. The next chart displays the result of that survey.

Number absences per term Actual number of students
0 - 2 35
3 - 5 40
6 - 8 20
9 - 11 1
12+ 4

Determine the null and alternate hypotheses needed to conduct a goodness-of-fit test.

H o : Student absenteeism fits faculty perception.

The alternate hypothesis is the opposite of the null hypothesis.

H a : Student absenteeism does not fit faculty perception.

Can you use the information as it appears in the charts to conduct the goodness-of-fit test?

No. Notice that the expected number of absences for the "12+" entry is less than 5 (it is 2). Combine that group with the "9 - 11" group to create new tables where the number of students for each entry are at least 5. The new tables are below.

Number absences per term Expected number of students
0 - 2 50
3 - 5 30
6 - 8 12
9+ 8
Number absences per term Actual number of students
0 - 2 35
3 - 5 40
6 - 8 20
9+ 5

Got questions? Get instant answers now!

What are the degrees of freedom ( df )?

There are 4 "cells" or categories in each of the new tables.

df = number of cells - 1 = 4 - 1 = 3

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Employers particularly want to know which days of the week employees are absent in a five day work week. Most employers wouldlike to believe that employees are absent equally during the week. Suppose a random sample of 60 managers were asked on which day of the week did they have the highest number of employee absences. The results were distributed as follows:

Day of the week employees were most absent
Monday Tuesday Wednesday Thursday Friday
Number of Absences 15 12 9 9 15

Questions & Answers

how can chip be made from sand
Eke Reply
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
Nerisha Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics' conversation and receive update notifications?

Ask