A two-way analysis of variance experiment with interaction was conducted. Factor

Question

A two-way analysis of variance experiment with interaction was conducted. Factor A had three levels (columns), factor B had five levels (rows), and six observations were obtained for each combination. The results include the following sum of square terms: SST = 1.572 SSA = 1.038 SSB = 346 SSAB = 33. Use a. Construct an ANOVA table. (Leave no cells blank - be certain to enter "0" wherever required. Round "p" value to 3 decimal places and all other answers except "df and *'SS" to 2 decimal places.) b. At the 1 % significance level, can you conclude that there is interaction between factor A and factor B? Yes, since the p-value associated with interaction is less than a. Yes, since the p-value associated with interaction is greater than a. No, since the p-value associated with interaction is less than a. No, since the p-value associated with interaction is is greater than a. c. At the 1% significance level, can you conclude that the factor A means differ? Yes. since the p-value for Factor A is less than a. Yes. since the p-value for Factor A is greater than a. No, since the p-value for Factor A is less than a. No, since the p-value for Factor A is greater than a. d. At the 1 % significance level, can you conclude that the factor B means differ? Yes. since the p-value for Factor B is less than a. Yes. since the p-value for Factor B is greater than a. No, since the p-value for Factor B is less than a. No, since the p-value for Factor B is greater than a.

Explanation / Answer

a)

b)

No since the p value for interaction is greater then alpha

c)

Yes since the p value for A is less then alpha

d)Yes since the p value for B is less then alpha

soucre SS df MS F p value F crit 1% rows 346 4 86.500 41.855 0.000 3.580 columns 1038 2 519.000 251.129 0.000 4.900 Interaction 33 8 4.125 1.996 0.058 2.758 error 155 75 2.067 total 1572 89

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