Casts of aluminum were subjected to four standard heat treatments and their tens
ID: 3024462 • Letter: C
Question
Casts of aluminum were subjected to four standard heat treatments and their tensile strengths were measured. Five measurements were taken on each treatment, with the results (in 1000 psi), Shown below.
Treatments
A
B
C
D
35
41
42
31
31
40
49
32
40
43
45
30
36
39
47
32
32
45
48
34
Perform an Analysis of variance (ANOVA). Do the mean tensile strengths differ from treatment to treatment, at 5 % significance level.
Find the critical value for this experiment.
Treatments
A
B
C
D
35
41
42
31
31
40
49
32
40
43
45
30
36
39
47
32
32
45
48
34
Explanation / Answer
Using technology (like Excel), we run a one-way anova to get this summary:
Hence, the critical value is
Fcrit = 3.2388 [ANSWER]
******************
As we can see, the P value is
P = 8.53*10^-7, which is much less than 0.05.
Hence, YES, THE TENSILE STRENGTHS DIFFER FROM TREATMENT TO TREATMENT AT 0.05 LEVEL. [CONCLUSION]
Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 5 174 34.8 12.7 Column 2 5 208 41.6 5.8 Column 3 5 231 46.2 7.7 Column 4 5 159 31.8 2.2 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 637.2 3 212.4 29.91549 8.53E-07 3.238872 Within Groups 113.6 16 7.1 Total 750.8 19Related Questions
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