Start-up Review Problems-- Ed257 D Rogosa January 2001 1. Complete the Anova Table given below. Also state and carry out a test of the omnibus null hypothesis with Type I error rate .10. SOURCE SS df MS Between 80 4 ** Within ** * ** Total 480 44 -------------------------------------------------------------------------- 2. Salary disputes and their eventual resolutions often leave both employer and employees embittered by the entire ordeal. To assess employee reactions to a recently devised salary and fringe benefits plan, the personnel department obtained random samples of 15 employees from each of three divisions: manufacturing, marketing, and research. Each employee sampled was asked to respond (in confidence) to a series of questions. Several employees refused to cooperate, as reflected in the unequal sample sizes. Some data summary is given below. Manufacturing Marketing Research Sample Size 12 14 11 Sample mean 25.2 32.6 28.1 Sample Variance 3.6 4.8 5.3 a. Write a model for this data structure b. Carry out an omnibus test of all three employee groups having equal population means using a standard one-way analysis of variance procedure. Use Type 1 error rate .01. ---------------------------------------------------------------------------- 3. I've had more knee operations than you've have had statistics courses.... From Neter Wasserman Kutner problem 16.12 A rehabililitation center researcher was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy until sucessful rehabilitation. 24 male subjects ranging in age from 18 to 30 years who had undergone similar corrective knee surgery during the past year were selected for the study. In the data file knee.dat in the class HW directory [note path is /afs/ir.stanford.edu/class/ed257/HW or /usr/class/ed257/HW ] c1 contains the number of days required for sucessful completion of physical therapy and c2 contains an indicator of prior physical fitness status-- 1 = below average; 2 = average; 3 = above average. (So this data set is of the form of a time-to-mastery study.) a) obtain mean and variance of time to recovery for each group b) present a graphical look at the scores for the three groups by constucting aligned dotplots for the three groups c) carry out an anova for this one-way classification and test the omnibus null hypothesis of no differences between the group means using Type I error rate .05. d) display residuals from the fit of the anova model for each group. --------------------------------------------------------------------- 4. Problem 1 from Review Problems (Jan '96) Could You Get In? The director of admissions at a small college administered a newly designed entrance test to 20 students randomly selected from the new freshman class. The purpose was to study the relation between the entrance test (in C2) and first year grade point average (GPA in C1). Minitab output given below. MTB > plot c1 c2 - * C1 - * - - * 3.20+ * - * * - * * - - * * 2.40+ - * * * - * * - * - * 1.60+ * - * * - ------+---------+---------+---------+---------+---------+C2 4.00 4.50 5.00 5.50 6.00 6.50 MTB > regress c1 on 1 c2 The regression equation is C1 = - 1.70 + 0.840 C2 Predictor Coef Stdev Constant -1.6996 0.7268 C2 0.8399 0.1440 s = 0.4350 R-sq = 65.4% MTB > regress c2 on 1 c1 The regression equation is C2 = 3.05 + 0.778 C1 Predictor Coef Stdev Constant 3.0539 0.3467 C1 0.7785 0.1335 s = 0.4188 R-sq = 65.4% a. Using the scatterplot, give values for the median and quartiles of GPA. b. Use the entrance test to predict GPA. From the least-squares fit computed by Minitab, what is the predicted GPA for a student scoring 5.0? What is the residual from the fit for a student scoring 6.0 on the entrance exam? c. If the mean of the entrance exam scores is 5.0, what is the mean GPA? d. What's the correlation between GPA and the entrance exam? NOTE the data reside in the class HW directory as admit.dat. Try to reproduce the simple output above using Minitab. ------------------------------------------------------ 5. An experiment was run in which a tumor was induced in a laboratory animal. The size of the tumor was recorded as Number of Days Size of Tumor After Induction (cc) 14 1.15 16 1.90 19 4.75 21 5.45 23 7.53 26 14.5 28 16.7 30 21.0 33 27.1 35 30.3 37 40.5 41 51.4 (You may want to "snip" these data out of this text for the analysis) Use a polynomial regression model to carry out a test of the curvilinear fit versus a straight line model? I.e., can you detect curvature in these data? -------------------------------------------------------- 6. The 2x2 table below cross-classifies level of education (rows) and voting intention (columns). Compute a measure of association between these two variables and test whether the association is different from zero. Will Vote Not Vote Some HS 1481 132 No HS 1036 173 ----------------------------------------------------------------------