Question

The mean quantity of milk produced by Guernsey and Holstein cows at Cold Comfort Farm is about the same, but the variation in output is quite a bit different as shown by the standard deviation of breed output from a sample of 10 Guernsey & 15 Holstein : σGuernsey = 1.8 and σHolstein = 1.2 Conduct an ANOVA F test to see if the Guernsey variation is really different from Holstein or simply due to pure chance. Use α = .05.

Answer 1

Let us denote 1 as Guernsey and 2 as Cold Comfort.

Given that

and

The test statistic is follows

The critical region for a two tailed test is

Since the calculated value of F falls in the rejection region, we reject the null hypothesis. Hence, we conclude that there is enough evidence that t Guernsey variation is really different from Holstein