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	35	28
	21	36	33
	33	39	33
	36	28	35
	29	32	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 -value is - Select your answer

-less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 12

What is your conclusion?

- Select your answer

-Conclude that the mean yields for the three temperatures are not all equalDo not reject the assumption that the mean yields for the three temperatures are equalItem 13

Answer 1

a)

Answer:

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	P-value
Treatments	43.33	2	21.67	1.10	0.3637
Error	236	12	19.67	.	.
Total	279.33	14	.	.	.

Explanation:

The one way ANOVA analysis is performed in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below

Step 2: DATA > Data Analysis > ANOVA: Single Factor > OK.  The screenshot is shown below,

Step 3: Select Input Range: All the data values column. The screenshot is shown below,

The result is obtained.  The screenshot is shown below,

b)

Answer:

F-value = 1.10

The P-value is greater than 0.10

Do not reject the assumption that the mean yields for the three temperatures are equal

Explanation:

A single factor ANOVA is used in excel to test the null hypothesis that all the means are equal. The hypothesis is defined as,

Null Hypothesis:  All the group means are equal,  

Alternative Hypothesis: At least one group mean differ significantly.

From the ANOVA table obtained in part a,

The F-value = 1.101695

The P-value = 0.363693

Since the P-value is greater than 0.10, the null hypothesis is not rejected at a 1% significance level. Hence there is not sufficient evidence to conclude that the group means are different.