To study the effect of temperature on yield in a chemical process, five batches
ID: 3242561 • Letter: T
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 32 34 29 22 35 34 34 38 34 37 27 36 30 31 37 Construct an analysis of variance table (to 2 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments 1 2.5 .12 Error 4 19.25 Total 97.5 5 Use a .05 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?
Explanation / Answer
50C
60C
70C
32
34
29
22
35
34
34
38
34
37
27
36
30
31
37
We go to excel then we select Data option. We go to Data Analysis. There we select the single factor Anova. We select the data set and we get the Analysis of Variance table as below:
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Column 1
5
155
31
32
Column 2
5
165
33
17.5
Column 3
5
170
34
9.5
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
23.33
2
11.67
0.59
0.57
3.89
Within Groups
236.00
12
19.67
Total
259.33
14
Null and Alternative Hypothesis:
H0: The temperature level has no effect on the mean yield of the process.
H1: The temperature level has n an effect on the mean yield of the process.
Level of significance = .05
Test Statistics: F = 0.59
P-value = 0.57
Here the p-value is greater than the level of significance (0.57>0.05); we fail to reject the null hypothesis.
Conclusion:
At 5% level of significance there is not sufficient evidence to conclude that the temperature level has an effect on the mean yield of the process.
50C
60C
70C
32
34
29
22
35
34
34
38
34
37
27
36
30
31
37
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