Question

I'm evaluating five identical burger restaurants over the last 7 weeks of business. I am trying to figure out if there is difference in the mean number of burgers sold among the 5 restaurants when the week is considered. The following information is given but incomplete and there are no replicates.

Given: restaurant = treatments, week = block

If my SS treatment = 400, SS error = 540 and SS Total = 1000. At a 0.05 level of significance, I would reject Ho for the treatment mean (restaurants) if my F calculated > F critical.

My F critical is found to be

(PLEASE SHOW WORK)

Answer 1

To find the critical value of F distribution, we need to find the degree of freedom.

Numerator degree of freedom = Number of levels of treatments - 1 = 5 - 1= 4

Denominator degree of freedom = Number of observations - Number of levels of treatments = 7 * 5 - 5 = 30

At a 0.05 level of significance, critical value of F at df = 4, 30 is 2.69

MS Treatment = SS treatment / Numerator degree of freedom = 400 / 4 = 100

MS error = SS error / Denominator degree of freedom = 540 / 30 = 18

F = MS Treatment / MS error = 100 / 18 = 5.56

Since, F calculated > F critical., we can reject Ho and conclude that there is significant evidence of difference in the mean number of burgers sold among the 5 restaurants