The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the
test for homogeneity , can be used to draw a conclusion about whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence.
Note
The expected value for each cell needs to be at least five in order for you to use this test.
Hypotheses
H
0 : The distributions of the two populations are the same.
H
a : The distributions of the two populations are not the same.
Test statistic
Use a
test statistic. It is computed in the same way as the test for independence.
Degrees of freedom (
df )
df = number of columns - 1
Requirements
All values in the table must be greater than or equal to five.
Common uses
Comparing two populations. For example: men vs. women, before vs. after, east vs. west. The variable is categorical with more than two possible response values.
Do male and female college students have the same distribution of living arrangements? Use a level of significance of 0.05. Suppose that 250 randomly selected male college students and 300 randomly selected female college students were asked about their living arrangements: dormitory, apartment, with parents, other. The results are shown in
[link] . Do male and female college students have the same distribution of living arrangements?
Distribution of living arragements for college males and college females
Dormitory
Apartment
With Parents
Other
Males
72
84
49
45
Females
91
86
88
35
H
0 : The distribution of living arrangements for male college students is the same as the distribution of living arrangements for female college students.
H
a : The distribution of living arrangements for male college students is not the same as the distribution of living arrangements for female college students.
Degrees of Freedom (
df ): df = number of columns – 1 = 4 – 1 = 3
Distribution for the test:
Calculate the test statistic:χ2 = 10.1287 (calculator or computer)
Probability statement:p -value =
P (
χ2 >10.1287) = 0.0175
Press the
MATRX key and arrow over to
EDIT . Press
1:[A] . Press
2 ENTER 4 ENTER . Enter the table values by row. Press
ENTER after each. Press
2nd QUIT . Press
STAT and arrow over to
TESTS . Arrow down to
C:χ2-TEST . Press
ENTER . You should see
Observed:[A] and Expected:[B] . Arrow down to
Calculate . Press
ENTER . The test statistic is 10.1287 and the
p -value = 0.0175. Do the procedure a second time but arrow down to
Draw instead of
calculate .
Compare
α and the
p -value: Since no
α is given, assume
α = 0.05.
p -value = 0.0175.
α >
p -value.
Make a decision: Since
α >
p -value, reject
H
0 . This means that the distributions are not the same.
Conclusion: At a 5% level of significance, from the data, there is sufficient evidence to conclude that the distributions of living arrangements for male and female college students are not the same.
Notice that the conclusion is only that the distributions are not the same. We cannot use the test for homogeneity to draw any conclusions about how they differ.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
