Question

M14 #16: A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars).

I	II	III
49.4	55.4	39.0
43.7	25.0	37.5
32.5	41.5	10.5
27.6	29.7	32.9
38.3	39.3	15.6
36.7		42.3
20.2

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

	I	II	III
count, ni =	7	5	6
mean , x̅ i =	35.48571429	38.18	29.63
std. dev., si =	9.79139564	11.7731474	13.29476087
sample variances, si^2 =	95.87142857	138.607	176.7506667
total sum	248.4	190.9	177.8		617.1	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				34.28
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	1.445719955	15.18	21.6225
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	10.12003968	75.92	129.735		215.7751
SS(within ) = SSW = Σ(n-1)s² =	575.2285714	554.43	883.7533333		2013.41

A)

SSbet = 215.775

SSW=2013.410

SST=Σ( x - x̅̅ )² =    2019.178

SS_BET + SS_W   = 215.775 + 2013.410 = 2019.178

B)

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   18
df within = N-k =   15
  
mean square between groups , MSB = SSB/k-1 =    107.8875
  
mean square within groups , MSW = SSW/N-k =    134.2273

C)

F-stat = MSB/MSW =    0.80

anova table
	SS	df	MS	F
Between:	215.775	2	107.8875	0.80
Within:	2013.410	15	134.2273
Total:	2229.185	17