TEST 3A AP Statistics Name: Directins: Wrk n these sheets. A standard nrmal table is attached. Part 1: Multiple Chice. Circle the letter crrespnding t the best answer. 1. In a statistics curse, a linear regressin equatin was cmputed t predict the final exam scre frm the scre n the first test. The equatin was y = 10 +.9x where y is the final exam scre and x is the scre n the first test. Carla scred 95 n the first test. What is the predicted value f her scre n the final exam? (a) 95 (b) 85.5 (c) 90 (d) 95.5 2. Refer t the previus prblem. On the final exam Carla scred 98. What is the value f her residual? (a) 98 (b) 2.5 (c) 2.5 (d) 0 3. A study f the fuel ecnmy fr varius autmbiles pltted the fuel cnsumptin (in liters f gasline used per 100 kilmeters traveled) vs. speed (in kilmeters per hur). A least squares line was fit t the data. Here is the residual plt frm this least squares fit. What des the pattern f the residuals tell yu abut the linear mdel? (a) The evidence is incnclusive. (b) The residual plt cnfirms the linearity f the fuel ecnmy data. (c) The residual plt des nt cnfirm the linearity f the data. (d) The residual plt clearly cntradicts the linearity f the data. 4. All but ne f the fllwing statements cntains a blunder. Which statement is crrect? (a) There is a crrelatin f 0.54 between the psitin a ftball player plays and their weight. (b) The crrelatin between planting rate and yield f crn was fund t be r=0.23. (c) The crrelatin between the gas mileage f a car and its weight is r=0.71 MPG. (d) We fund a high crrelatin (r=1.09) between the height and age f children. (e) We fund a crrelatin f r=.63 between gender and plitical party preference. Chapter 3 1 Test 3A
Part 2: Free Respnse Answer cmpletely, but be cncise. Write sequentially and shw all steps. 5. Briefly explain the cartn. He says we ve ruined his psitive assciatin between height and weight. Exercises 6 9 relate t the fllwing. Jey read in his bilgy bk that fish activity increases with water temperature, and he decided t investigate this issue by cnducting an experiment. On nine successive days, he measures fish activity and water temperature in his aquarium. Larger values f his measure f fish activity dente mre activity. The figure belw presents the scatterplt f his data. 450 Activity 300 69.0 72.0 75.0 78.0 81.0 6. What des the scatterplt reveal? Chapter 3 2 Test 3A
7. One f the fllwing numbers is the crrelatin cefficient between fish activity and water temperature; circle the crrect number. 0.20 0.03 0.52 0.86 8. Write yur best guess fr the crrelatin cefficient fr water temperature versus fish activity. Then briefly explain yur reasning. 9. Suppse a new pint at (66, 500), i.e., water temperature = 66 F and fish activity = 500, is added t the plt. Describe the effect, if any, that this new pint will have n the crrelatin cefficient f fish activity versus water temperature? Exercises 10-14 relate t the fllwing. At summer camp, ne f Carla s cunselrs tld her that air temperature can be determined frm the number f cricket chirps. 10. What is the explanatry variable, and what is the respnse variable? (Nte: this is in the cntext f this prblem, nt in the bilgical sense.) EXPLANATORY: RESPONSE: T determine a frmula, Carla cllected data n temperature and number f chirps per minute n 12 ccasins. She entered the data int lists L1 and L2 f her TI-83 and then did STATS CALC 2-Var Stats. Here are sme f the results: x = 166.8, s x = 31.0 y = 78.83 s y = 9.11 r = 0.461 11. Use this infrmatin t determine the equatin f the LSRL. Chapter 3 3 Test 3A
12. One f Carla s data pints was recrded n a particularly ht day (93 F). She cunted 249 cricket chirps in ne minute. What temperature wuld Carla s mdel predict fr this number f cricket chirps? (Rund t the nearest degree.) 13. What is the residual fr the data pint in exercise 12? 14. Suppse that Carla cunted 249 chirps n a day when the temperature was 55 F. If this pint were the 13th data pint, what effect, if any, wuld this 13th pint have n Carla s LSRL? Explain briefly. 15. In general, is crrelatin a resistant measure f assciatin? Explain briefly r give a simple example t illustrate. 16. Is the least-squares regressin line resistant? Explain briefly r give a simple example t illustrate. I pledge that I have neither given nr received aid n this test. Chapter 3 4 Test 3A