2} A researcher at a pet food manufacturer has designed a study to test new flavors of cat kibble: Salmon, Chicken, Liver, and Giblets. 26 cats were recruited for the study, and they were randomly assigned to four groups: 6 cats were fed the Salmon flavor; 7 cats were fed the Chicken flavor; 6 cats were fed the Liver flavor; and 7 cats were fed the Giblets flavor. The amount of food the cats ate was measured, in grams. Here are the sample statistics calculated by the researcher: Sample Mean Amount Sample Variance 0f of Food Eaten Amount of Food Eaten Perform an ANOVA at the a : 0.05 significance level to determine whether any of the groups ate a different population mean amount than the others. Since this study utilized random assignment, it can prove cause and effect. Did any ofthe flavors cause the cats to eat a different amount of food than the others? ANOVA Summary Table (2 points) Critical p-value Value of F of Fm, For each problem, show at minimum: 1) 2) The null and alternative hypotheses, written using proper notation (2 points) The test statistic calculation showing: a. For the first problem, show the letter ofthe test statistic, the formula for the test statistic, the numbers filled into the formula, and the final result. Round the test statistic to three decimals. (3 points) b. For the second problem, show your work. Keep intermediate calculations at four decimals. Round the test statistic to three decimals. (5 points) The rejection step showing BOTH the p-value approach (2 points) AND the CV approach (2 points}. You do not need to draw the rejection diagram unless you want to. You must show the proper p- value (to four decimals) and proper CV or CVs, and the rejection rule (whether in numbers or with the diagram) that led you to your decision about the null hypothesis. State what happened to the null and the alternative hypotheses to get full credit. Interpret the test result, referencing the alpha significance level (or percent confidence level}, and answering all questions asked. (3 points) Be sure to fill out the ANOVA Summary Table (2 points)