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
	34	32	22
	24	33	27
	36	36	27
	39	25	29
	32	29	30

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.
   
   The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 11  
   
   What is your conclusion?
   SelectConclude that the mean yields for the three temperatures are not all equalConclude that the mean yields for the three temperatures are all equalItem 12

Answer 1

The statistical software output for this problem is:

Analysis of Variance results: Data stored in separate columns. Column statistics ColumnnMean. Std. Dev.Std. Error 50°C 60°C 70°C 33 5.6568542 2.5298221 31 4.1833001 1.8708287 5 27 3.082207 1.3784049 ANOVA table F-StatP-value Source DF SS Columns2 93.333333 46.666667 2.3728814 0.1354 Error 12 Total14 329,33333 MS 236 19.666667

Hence,

a) ANOVA table will be:

Source	SS	DF	MS	F-Stat	P-value
Treatment	93.33	2	46.67	2.37	0.1354
Error	236	12	19.67
Total	329.33	14

b) p - value is greater than 0.10

c) Conclude that the mean yields for the three temperatures are all equal.