Introduction to Statistics Practice Final Examination

Introduction to Statistics Practice Final Examination 1) In an experiment on honesty, each subject waited in a room with a bowl of candy and was told to help him/herself to one and only one piece. Subjects sat in the room either by themselves, or with one other person; the experimenter randomly decided whether a subject sat alone or with another person. A hidden camera recorded the number of pieces of candy taken by each subject after the experimenter left the room. Subjects who waited by themselves ate an average of 1.7 pieces of candy. Subjects who waited with another person ate an average of 1.2 pieces of candy. A t-test yielded an observed value of 3.25, and a p-value of .02 (2 pts each). a) Is this an observational or designed experiment? Explain. b) What is/are the independent variable(s)? c) What is/are the dependent variables(s)? d) List all descriptive statistics. e) List all of the inferential statistics. f) If the t-test reported above was a two-tailed test, what would the p-value be for a one-tailed test? g) What is the null hypothesis for the test described above? 2) My favorite TV show (Blind Date: which was on at night in IL, but only during the day here in MA; major bummer) is constantly interrupted by commercials for various Psychic Hotlines. Most people would ignore this nonsense, but is that good enough for us? No. We want to know whether there is anything to this tomfoolery. So, we call each of three hotlines 5 times and ask the same question: What day during the month of June was I married? According to my wife (who seems to remember these kinds of things), the answer is the 17th. The data below indicate the number of days off for each psychic. Conduct a One-Way ANOVA to determine if the three Psychic Hotlines differ in terms of the accuracy of their psychics (Fcrit = 3.88). Your answer should include a statement of the null and alternative hypotheses, the observed value for F, your decision regarding the null (with explanation), and an interpretation of what your decision means in terms of the relative accuracy of the various psychic hotlines (16 pts). Psychic Psychic Psychics of Friends Enemies the New Millenium 13 7 6 11 8 9 12 5 13 13 6 16 16 4 11 b) Calculate Tukey's Honestly Significant Difference (qcrit = 3.77) to determine which levels of the IV are different from one another. (4 pts) 3) The Illinois State Department of Transportation is concerned about the number of overloaded minivans that will be clogging the northbound lanes of I-57 over the next couple of weeks. They commissioned a study to examine the amount of junk (in pounds) brought home by Illinois students at the end of the semester. In particular, they were interested in the effect of gender (Male vs. Female) and class (Frosh vs. Senior) on the total weight of junk. The data were submitted to a 2x2 ANOVA (including a Gender x Class interaction). Use the SAS output below to answer the following questions. Assume  = .05. Source Model Error Total df Source Gender Class G*C df 1 1 1 Sums of Squares 342.00 Mean Square F p-value .0257 F p-value .0125 .0327 .0001 4.50 79 Sums of Squares 27.00 36.00 117.00 Mean Square 27.00 36.00 117.00 8.00 Mean Packing Weights Males Females Frosh 150 200 Seniors 175 500 a) Fill in the blanks for the ANOVA table above (1 pt each). b) Determine whether there is a significant effect of Gender, of Class, and of the G*C interaction. Interpret each of these findings (10 pts). 4) This summer you got stuck with a stinky telemarketing job selling Aluminum Siding. Your bosses keep track of how many hours you work and how many sales you make. They are interested in determining if there is a relationship between Hours and Sales. Below are the data for you and four of your groovy co-workers (Chris got a job at the car wash). Employee Hours last Sales x2 xy shift JC 3 31 Lance 4 50 Justin 5 64 You 8 95 Joey 10 106 x y (x2) (xy) a) Calculate the regression equation suggested by the data (12 pts)? b) Would you conclude that Hours helped predict Sales if a t-test revealed that 0 was significantly different from 0? Explain (2 pts). c) Would your answer to part b) change if a t-test revealed that 1 was also significantly different from 0? Explain (2 pts). d) Based on the regression equation, are you a relatively good salesperson, or a relatively poor salesperson? Explain (2 pts). e) What is r? 5) I have decided to try to make some money by predicting the winner of the 2nd leg of the Triple Crown, the Preakness Stakes. I use the data from 80 previous entrants in the race determine what factors predict the place a horse finishes (1st, 2nd, 3rd, etc.). I used the following 6 factors: # of races won by the horse (WINS), # of races won by the horse's PARENTS, HEIGHT (in hands), WEIGHT of the jockey (in kg), SPEED (average time to run 1/4 mile), and ENDURANCE (average time to run 1 mile). Base your answer to the following questions on the SAS output below (3 pts each). Source df SS MS F p-value Model 6 370.71 61.79 9.95 .0168 Error 73 453.09 6.21 Total 79 823.80 Variable Intercept Wins Parents Height Weight Speed Endurance df 1 1 1 1 1 1 1 Param Est. 2.80 -0.25 -0.37 0.08 0.02 0.03 0.03 Std Err 0.54 0.05 0.82 0.04 0.01 0.01 0.03 t 5.22 -5.02 -4.50 2.17 3.05 -4.86 -1.12 p-value .0053 .0088 .0176 .0821 .0486 .0271 .4462 a) What is the regression equation suggested by this analysis? b) Does the regression analysis suggest that this model will be helpful in predicting the winner of the Preakness? Explain. c) How much of the variance in y (predicted finish) can we explain with our model? d) Mr. Ed (Wins = 0, Parents = 1, Height = 15, Weight = 53, Speed = 17, Endurance = 60) is likely to compete in the Preakness. In what place would you predict Mr. Ed to finish?