Question

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.

Temperature
	50°C	60°C	70°C
	33	29	27
	23	30	32
	35	33	32
	38	22	34
	31	26	35

1. Construct an analysis of variance table (to 2 decimals, if necessary). Round p-value to four decimal places.
   

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Treatments
   Error
   Total

   
   
2. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process.

Answer 1

treatment	A	B	C
count, ni =	5	5	5
mean , x̅ i =	32.000	28.00	32.000
std. dev., si =	5.657	4.183	3.082
sample variances, si^2 =	32.000	17.500	9.500
total sum	160	140	160		460	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	30.67
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	1.778	7.111	1.778
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	8.889	35.556	8.889		53.33333333
SS(within ) = SSW = Σ(n-1)s² =	128.000	70.000	38.000		236.0000

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   15
df within = N-k =   12
  
mean square between groups , MSB = SSB/k-1 =    26.6667
  
mean square within groups , MSW = SSW/N-k =    19.6667
  
F-stat = MSB/MSW =    1.3559

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	53.33	2	26.67	1.36	0.2945	3.89
Within Groups	236.00	12	19.67
Total	289.33	14

b)

   Decision:   p-value>α , do not reject null hypothesis    
there is no enough evidence that  the temperature level has an effect on the mean yield of the process.