An analysis of variance is used to evaluate the mean differe

An analysis of variance is used to evaluate the mean differences for a research study comparing four treatments with a separate sample of n = 8 in each treatment. If the data produce an F-ratio of F = 4.60, which of the following is the correct statistical decision

Solution

There are four treatments so k=4 and since each sample has 8 observations so total number of observations so N=4*8=32. Therefore degree of freedom of numerator of f-test is df1=k-1=3

and degree of freedom of denominator is

df2=N-k=32-4=28

So p-value of the test for df1=3, df2= 28 and F = 4.60 is 0.0097.

Since p-value is less than 0.01 level of significance, so we reject the null hypothesis. That is result is significant.