Lauren Perry

Lauren Perry

Assistant Professor of Mathematics & Statistics at Sacramento State
Pronouns: she/her

Homework 4: Due October 24

Homework 4: Due October 24

Homeworks should be done on paper with a physical copy turned in to your TA at the start of discussion. Grading will be based on completeness as well as accuracy. In order to receive credit, you must show all your work. If you need critical/p values, you may use R, your textbook, or an applet such as the one by Stak Trek.

Note: the materials for Week 4 come from Introduction to Probability and Statistics by Mendenhall, Beaver, & Beaver. If you choose to reference this textbook, be aware that their notation is slightly different from that used in the OpenIntro Statistics text.

  1. The following data were obtained for a randomized block design with five treatments and three blocks: SST = 430, SSG = 310, SSB = 85. Set up the ANOVA table and test for any significant difference at the 0.05 level of significance.

  2. Five different auditing procedures were compared with respect to total audit time. To control for possible variation due to the person conducting the audit, four accountants were selected randomly and treated as blocks in the experiment. The following values were obtained using the ANOVA procedure: SST = 100, SSG = 45, SSB = 36. Test at the 0.05 level of significance if there are any signifiant differences in mean total audit time between the different auditing procedures.

  3. The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following: SST = 280, SSA = 26, SSB = 23, SSAB = 175. Set up the ANOVA table and test for any significant main effects and any interaction effect. Test at the 0.05 level of significance.

  4. In your own words, explain what the analysis of variance is used for. Why is it called the analysis of variance?

  5. A statistics professor wishes to know the effect of class format on student learning, as measured by exam score improvement from beginning to end of quarter. The five class formats to be studied reflect different levels of emphasis on homework problems, computer exercises, and online videos. Sixty students are randomly selected for this study. What type of experimental design would you recommend for this problem? Why?

  6. Now suppose each of the class formats are to be studied in a high school setting and in a university setting. Sixty high school students and sixty college students are randomly selected for this study. What type of experimental design would you recommend for this problem? Why?

  7. Finally, suppose you have access to sixty randomly selected university students and want to examine the five class formats. What are some possible blocks that might be of interest? What are some possible factors?