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 30 29 28 20 30 33 32 33 33 35 22 35 28 26 36 a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total 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

a)

Null hypothesis H0: All means are equal

i.e. temperature level has not an effect on the mean yield of the process

Alternative hypothesis H1:   Not all means are equal

i.e. temperature level has an effect on the mean yield of the process

Significance level   α = 0.05

Equal variances were assumed for the analysis.

From the given data

		Total	Ti^2/ni
50°C	30	20	32	35	28	145	4205
60°C	29	30	33	22	26	140	3920
70°C	28	33	33	35	36	165	5445
					Total G	450	13570

P-value = 0.2105

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

H0:

H1: temperature level has an effect on the mean yield of the process

Test Statistic = 1.78

The p-value is 0.2105 > alpha 0.05 so we accept H0

thus we conclude that All means are equal i.e. temperature level has not an effect on the mean yield of the process