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Using a two-way ANOVA

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Two types of outdoor paint, enamel and latex, were tested to see how long (in months) each lasted before it began to crack, flake, and peel. They were tested in four geographic locations in the US to study the effects of climate on the paint. At gamma = 0.01, analyze the data shown, using a two-way ANOVA shown below. Each group contained five test panels. See below for raw data.
Enamel
North: 60, 53, 58, 62, 57
East: 54, 63, 62, 71, 76
South: 80, 82, 62, 88, 71
West: 62, 76, 55, 48, 61
Latex
North: 36, 41, 54, 65, 53
East: 62, 61, 77, 53, 64
South: 68, 72, 71, 82, 86
West: 63, 65, 72, 71, 63
ANOVA Summary
Source - SS - df - MS - F
Paint type - 12.1
Location - 2501.0
Interaction - 268.1
Within - 2326.8
Total - 5108.0.

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Solution Summary

The solution uses a two-way ANOVA.

Solution Preview

Below is the complete ANOVA table (see the spreadsheet)

ANOVA
Source of Variation SS df MS F P-value F crit
Paint ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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