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.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
