Question

Route 1	Route 2	Route 3
31	27	16
31	28	40
27	28	22
35	36	31

SS_between. (Round your answer to one decimal place.)
  

SS_within. (Round your answer to one decimal place.)


State the F statistic. (Round your answer to four decimal places.)

Answer 1

treatment	Route 1	Route 2	Route 3
count, ni =	4	4	4
mean , x̅ i =	31.000	29.75	27.250
std. dev., si =	3.266	4.193	10.500
sample variances, si^2 =	10.667	17.583	110.250
total sum	124	119	109		352	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	29.33
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	2.778	0.174	4.340
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	11.111	0.694	17.361		29.16666667
SS(within ) = SSW = Σ(n-1)s² =	32.000	52.750	330.750		415.5000

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   12
df within = N-k =   9
  
mean square between groups , MSB = SSB/k-1 =    14.5833
  
mean square within groups , MSW = SSW/N-k =    46.1667
  
F-stat = MSB/MSW =    0.3159

SS between=29.2

SS within=415.5

F=0.3159