1. F-Distribution : a. Compute P(F4,9 > 3.24). b. Suppose we have 6 populations

Question

1. F-Distribution :

a. Compute P(F4,9 > 3.24).

b. Suppose we have 6 populations we wish to compare. We are interested in testing whether all the populations have the same mean. Our data set contains 48 observations which are divided amongst the 6 populations evenly. Stata reports the test statistic to be F = 4.28.

i. How many degrees of freedom are in the numerator of the F-distribution?

ii. How many degrees of freedom are in the denominator of the F-distribution?

iii. Calculate the p-value for the test.

iv. Want can you conclude about the equality of the means from all of the

populations?

Explanation / Answer

a) From F probability calculator:

F(4, 9 > 3.24) = 0.0660

b) i) Numerator degrees of freedom = Number of populations - 1 = 6 - 1 = 5

ii) Denominator degrees of freedom = Number of observations - Number of populations = 48 - 6 = 42

iii) p - Value = P(F 5, 42 > 4.28) = 0.0031

iv) Since p - value is very small, we reject Ho. Hence,

There is strong evidence to conclude that not all population means are equal.

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