Exam 9: Design of Experiments and Analysis of Variance

A city monitors ozone levels weekly over a 3 year period in order to relate the ozone levels to the seasons. Determine whether the study is observational or designed.

307 diamonds were sampled and randomly sorted into three groups of diamonds. These diamonds were randomly assigned to one of the three organizations, or groups (HRD, GIA, or IGI), that certify the appraisal of diamonds. A study was conducted to determine if the average size of Diamonds reported by these three certification groups differ. A completely randomized design was used and the resulting ANOVA table is shown below. One-Way AOV for CARAT by CERT Source DF SS MS F P CERT 2 8.3265 4.16326 83.21 0.0000 Error 305 15.2604 0.05003 Total 307 23.5869 Specify the null hypothesis for a test to compare the mean size of a diamond for the three certification groups (HRD, GIA, and IGI).

A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 21 physicians from each of the three certification levels-Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)-and recorded the total per-member, per-month charges for each (a total of 63 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Give the degrees of freedom appropriate for conducting the ANOVA F-test.

An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 28 recently hired sales trainees were randomly assigned to one of 7 different "home rooms" - four trainees per room. Each room is identical except for wall color, with 7 different colors used. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the 7 room colors. At the end of the training program, the attitude of each trainee was measured on a 100-pt. scale (the lower the score, the poorer the attitude). How many treatments are in this study?

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets, A, B, and C. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, The prices were recorded for each item on the same day at each supermarket. Item 1 1) paper towels 1.24 1.44 1.39 2) cereal 2.73 3.18 2.93 3 ) floor cleaner 5.93 5.81 6.82 \vert \vert \vert \vert \vert 59) shaving cream 1.07 0.97 1.03 60 ) canned green beans 0.40 0.55 0.32 Identify the dependent (response) variable for this experiment.

The intensity of a factor is called __________.

Which of the following is not a condition required for a valid ANOVA F-test for a completely randomized experiment?