A12 anova.

Neatly respond to each prompt. Show all work for full credit. Round to four decimal places.

1. In ANOVA, _______ describes how much the sample means vary around the overall mean.

a. Between group variance

b. Within group variance

c. factor

2. Why do we examine variance to determine if there is a difference in means?

3. In a one-way ANOVA with 3 groups, a rejection of the null hypothesis implies that

a. the 3 population means are equal to each other

b. the 3 sample means are equal to each other

c. each population mean differs significantly from all other population means

d. each sample mean differs significantly from all other sample means

e. some subset of population means differs from some other subset of population means

f. some subset of sample means differs from some other subset of sample means

4. A psychologist is studying the effect of drug and electroshock therapy on a subject's ability to solve simple tasks. The number of tasks completed in a 10-minute period is recorded for subjects who have been randomly assigned to compare four treatment groups: drug with electroshock, drug without electroshock, no drug with electroshock, and no drug/no electroshock. Sixty-four subjects were randomly selected students from a large local university.

a. State the null and alternative hypotheses for the researchers.

b. Presented are the results from an Analysis of Variance run on these data. Explain to the psychologist what can be concluded from this analysis and how your conclusion follows from this output (assuming the technical conditions are met).

5. Recommendations regarding how long infants in developing countries should be breast-fed are controversial. If the nutritional quality of the breast milk is inadequate because the mother is malnourished, then there is risk of inadequate nutrition for the infant. One question related to this controversy concerns the amount of energy intake for infants who have other foods introduced into the diet at different ages. Part of one study compared the energy intakes, measured in kilocalories per day (kcal/d), for infants who were breast-fed exclusively for 4, 5, or 6 months. Researchers tested whether there was evidence of a statistically significant difference in the mean energy intake for these different groups.

a. Clearly state the appropriate null and alternative hypotheses for this analysis.

b. What should they conclude based on this output? Explain.

c. Would you be willing to generalize these results to infants in the United States? Explain.

6. A panel of trained testers judged the flavor quality of different vanilla frozen desserts (frozen yogurts, ice milks, other frozen desserts) measured on a scale from 0 to 100. The data are from a Consumer Reports article "Low-fat frozen desserts: Better for you than ice cream?" (August, 1992). Here is a graphical summary of the data.

a. Explain briefly why ANOVA was the appropriate analysis for these data.

b. Finish the ANOVA table giving the F-statistic, degrees of freedom, and approximating the p-value. Show your work. What is your conclusion about the flavor quality of the different desserts?

c. Based on the graph, do you have any concerns about the technical assumptions needed for the validity of this test procedure? Explain.