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.
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
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