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Homework answers / question archive / To be sure that the various batches of data arriving at the research center were from the same population, the director developed an analysis of variance
To be sure that the various batches of data arriving at the research center were from the same population, the director developed an analysis of variance. The variance among the means was 4.54 and contained three degrees of freedom. The variance within the data was 1.20 and contained 10 degrees of freedom. There were four batches in the analysis, and the director used the 95% reliability level.
State the hypothesis the director was attempting to prove.
Has he proven the hypothesis? Show all calculations....
So the null hypothesis is that the data all comes from the same sample
The alternative hypothesis is that that the data does not come from the same sample.
Next we have to calculate the f statistic.
Lets recap the data:
variance amongst means - 4.54
3 degrees of freedom
variance within the data is 1.2
10 degrees of freedom
We are lucky that all of this data is given to us already, since it is a very long process to calculate it.
You can use the data provided to calculate the final answers to give you F which is your test stat :
#1)Mean square among = variance amongst means/degree of freedom among = 4.54/3 =1.51
#2) Mean square within = variance within /degree of freedom within = 1.2/10 = 0.12
#3) F = variance amongst / variance within = 1.51/.12 = 12.58
All you have to do is compare that value with the critical value F (3,10) You have to look on a F-table to determine this value. from the table, the critical value is 8,79.
Since 12.58 is greater then 8,79, we can accept the null hypothesis, and conclude that the data did in fact come from the same population.
Please note that on the f-table, you look up the critical value by df2df1, where df2 (amongst) is on the horizontal access, and df1 is on the vertical access.
