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 United States to study the effects of climate on the paint. At α = 0.01, analyze the data shown, using a two-way ANOVA shown below. Each group contained five test panels. See below for raw data.
Data

ANOVA Summary Table

Perform these steps. Assume that all variables are normally or approximately normally distributed, that the samples are independent, and that the population variances are equal.
a. State the hypotheses.
b. Find the critical value for each F test.
c. Complete the summary table and find the test value.
d. Make the decision.
e. Summarize the results. (Draw a graph of the cell means if necessary.)

Transcribed Image Text:

Geographic location Type of paint Enamel Latex North 60, 53, 58, 62, 57 36, 41, 54, 65, 53 East 54, 63, 62, 71, 76 62, 61, 77, 53, 64 South West 62, 76, 55, 48, 61 63, 65, 72, 71, 63 80, 82, 62, 88, 71 68, 72, 71, 82, 86 Source d.f MS Paint type Location Interaction Within 12.1 2501.0 268.1 2326.8 5108.0 Total