Question

Where are the deer? Random samples of square-kilometer plots were taken in different ecological locations of a national park. The deer counts per square kilometer were recorded and are shown in the following table.

Mountain Brush	Sagebrush Grassland	Pinon Juniper
30	15	4
30	57	9
20	21	8
25	23	4

A)  Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

B) Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 4 decimal places for MS_BET, and MS_W.)

C) Find the value of the sample F statistic. (Use 2 decimal places.)

Answer 1

	Mountain Brush	Sagebrush Grassland	Pinon Juniper	Total
Sum	105	116	25	246
Count	4	4	4	12
Mean, Sum/n	26.25	29	6.25
Sum of square, Ʃ(xᵢ-x̅)²	68.75	1080	20.75
Standard deviation	4.787136	18.97367	2.629956

Number of treatment, k =        3
Total sample Size, N =       12
      
A) SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N =       1233.500
SS(within) = SS1 + SS2 + SS3 =        1169.500
SS(total) = SS(between) + SS(within) =       2403

B) df(between) = k-1 =       2
df(within) = N-k =      9
df(total) = N-1 =       11
      
MS(between) = SS(between)/df(between) =       616.75
MS(within) = SS(within)/df(within) =       129.9444
      
C) F = MS(between)/MS(within) =       4.75