A researcher wanted to test the effectiveness of three different fertilizers on crop yield, so she randomly assigned 45 plots of land to the three treatment groups, with 15 plots in each group. She then measured the crop yield (in bushels per acre) for each plot of land. The ANOVA summary table is partially filled as follows:
Source SS df MS F
Between 372.52 2 186.26 4.62
Within 42
Total 44
Perform an ANOVA and answer the following questions:
(a) What are the null and alternative hypotheses for this ANOVA?
(b) What is the critical value for F at a significance level of 0.05?
(c) What is the calculated F ratio for this ANOVA?
(d) What is the conclusion about the null hypothesis at a significance level of 0.05?
(e) What is the measure of effect size for this ANOVA?
(f) Write a summary of the conclusions that can be made from this study (including an interpretation of the null decision, effect size, and confidence interval).