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
	31	33	23
	21	34	28
	33	37	28
	36	26	30
	29	30	31

a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary).

b. Use a level of significance to test whether the temperature level has an effect on the mean yield of the process. Calculate the value of the test statistic (to 2 decimals). The p -value is?

What is your conclusion?

Answer 1

	50°C	60°C	70°C	Total
Sum	150	160	140	450
Count	5	5	5	15
Mean, Sum/n	30	32	28
Sum of square, Ʃ(xᵢ-x̅)²	128	70	38

Number of treatment, k = 3

Total sample Size, N = 15

df(between) = k-1 = 2

df(within) = N-k = 12

df(total) = N-1 = 14

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N = 40

SS(within) = SS1 + SS2 + SS3 = 236

SS(total) = SS(between) + SS(within) = 276

MS(between) = SS(between)/df(between) = 20

MS(within) = SS(within)/df(within) = 19.66667

F = MS(between)/MS(within) = 1.0169

p-value = F.DIST.RT(1.0169, 2, 12) = 0.3909

a)

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	40.00	2	20.00	1.02	0.3909
Within Groups	236.00	12	19.67
Total	276.00	14

b)

Test statistic:

F = 1.02

p-value = F.DIST.RT(1.0169, 2, 12) = 0.3909

Conclusion:

P-value > α, Do not reject the null hypothesis.

There is not enough evidence to conclude that the temperature level has an effect on the mean yield of the process.