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Answer:
p > α
0.7038 > 0.05
Also since F < F critical
0.475 < 3.238
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.
Step-by-step explanation:
We are given that a chemist wishes to test the effect of four chemical agents on the strength of a particular type of cloth.
Since we are given data for four independent chemical agents to determine the effect on the strength of a particular type of cloth, therefore, a one-way analysis of variance may be used for the given problem.
ANOVA:
The one-way analysis of variance (ANOVA) may be used to find out whether there is any significant difference between the means of two or more independent categories of data.
Set up hypotheses:
Null hypotheses = H₀: μ₁ = μ₂ = μ₃ = μ₄
Alternate hypotheses = H₁: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
Set up decision rule:
We Reject H₀ if p ≤ α
OR
We Reject H₀ if F > F critical
ANOVA in Excel:
Step 1:
In the data tab, select data analysis
Step 2:
Select "Anova single factor" from the analysis tools
Step 3:
Select the destination of input data in the "input range"
Step 4:
Select "rows" for the option "Group By"
Step 5:
Tick the option "labels in first row"
Step 6:
Set alpha = 0.05
Step 7:
Select the destination of output data in the "output options"
Conclusion:
Please refer to the attached results.
The p-value is found to be
p = 0.7038
The F value is found to be
F = 0.475
The F critical value is found to be
F critical = 3.238
Since p > α
0.7038 > 0.05
We failed to reject H₀
Also since F < F critical
0.475 < 3.238
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.
