Question

An experiment was performed to determine whether the annealing temperature of ductile iron affects its tensile strength. Five specimens were annealed at each of four temperatures. The tensile strength (in ksi) was measured for each. The results are presented in the following table.

Machine
Temperature(°C) Sample Values
750 17.89 16.01 16.66 16.93
800 19.72 20.04 14.49 18.10
850 17.38 14.49 20.88 15.53
90016.15 19.63 20.28 18.21 13.25
18.68 20.53 15.58
Perform the analysis of variance(ANOVA) at the 0.05 level of significance and indicate whether or not there are differences among the mean strengths?

Answer 1

There are significant differences among the mean tensile strengths for different temperatures.

Explanation:

A one-way ANOVA is used to test whether there is significant difference between the means for more than two groups.

The hypothesis can be defined as follows:

H₀: There is no difference between the means, i.e.
`\mu_(1)=\mu_(2)=\mu_(3)=\mu_(4)`.

Hₐ: There is a significant difference between the means, i.e.at least one of the mean is different.

Use MS-Excel to perform the analysis of variance.

Go to Data → Data Analysis → Anova: Single Factor.

A dialog box will open.

Enter the data and enter Alpha as 0.05.

Press OK.

The output is attached below.

The F-value is, 8.40458.

The p-value of the test is, 0.00139.

Decision Rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.00139 < α = 0.05

The null hypothesis will be rejected at 5% level of significance.

Concluding that there are differences among the mean tensile strengths for different temperatures.