AP Statistics Practice Test Unit Three Exploring Relationships Between Variables. Name Period Date

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1 AP Statistics Practice Test Unit Three Explring Relatinships Between Variables Name Perid Date True r False: 1. Crrelatin and regressin require explanatry and respnse variables Every least squares regressin line passes thrugh ( x, y ). 2. Shrt Answer: 3. In a simple, linear regressin mdel, the variable that is being predicted may be called which f the fllwing: (Check all that apply) _ independent variable _ regressin variable _ dependent variable _ respnse variable _ X variable _ Y variable 4. Which f the fllwing crrelatin values represents a perfect linear relatinship between tw quantitative variables? (Check all that apply) _ 0 _ 1 _.9 _.5 _ A psitive crrelatin between tw variables X and Y means: If yu increase the X value, this will cause the value f Y t increase. Circle the crrect answer and briefly explain. a. This is always true. b. This is smetimes true. c. This is never true. 6. Describe a situatin in which yu wuld expect a fairly strng assciatin between tw variables that d nt have a cause-and-effect relatinship. 7. Think f a set f bivariate, quantitative data. When the crrelatin cefficient fr these data is clse t 1, must the slpe als be clse t 1? Explain. 8. In the scatterplt f y versus x shwn at the right, circle the pint with the largest residual and place a square arund the pint that wuld be cnsidered an influential bservatin. 1

2 Multiple-Chice: Circle the best answer. 9. Which f these statements are false? (A) There is a strng linear relatinship between gender and height because we fund a crrelatin f.65. (B) Plant height and leaf height were fund t be negatively crrelated because the crrelatin cefficient is (C) Since the crrelatin between X and Y is 0, this means there is n relatinship whatsever between these tw variables. (D) All f the abve. (E) Nne f the abve. 10. Tw measures x and y were taken n 18 subjects. The first f tw regressins, Regressin I, yielded yˆ = x and had the fllwing residual plt. The secnd regressin, Regressin II, yielded plt. lg( yˆ ) = lg( x) and had the fllwing residual Which f the fllwing cnclusins is best supprted by the evidence abve? (A) There is a linear relatinship between x and y, and Regressin I yields a better fit. (B) There is a linear relatinship between x and y, and Regressin II yields a better fit. (C) There is a negative crrelatin between x and y. (D) There is a nnlinear relatinship between x and y, and Regressin I yields a better fit. (E) There is a nnlinear relatinship between x and y, and Regressin II yields a better fit. 11. There is a linear relatinship between the number f chirps made by the striped grund cricket and the air temperature. A least squares fit f sme data cllected by a bilgist gives the mdel yˆ x =, 9 < x < 25, where x is the number f chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that crrespnds t an increase f 5 chirps per minute? (A) 3.3 F (B) 16.5 F (C) 25.2 F (D) 28.5 F (E) 41.7 F 2

3 12. The equatin f the least squares regressin line fr the pints n the scatterplt at the right is yˆ = x. What is the residual fr the pint (4, 7)? (A) 2.78 (B) 3.00 (C) 4.00 (D) 4.22 (E) 7.00 y x 13. What des the pattern f the residuals tell yu abut the linear mdel? (A) The evidence is incnclusive. (B) The residual plt clearly cntradicts the linearity f the data. (C) The residual plt cnfirms the linearity f the fuel ecnmy data. (D) Nne f the abve. Free Respnse: Exercises 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. Act i vi t y What des the scatterplt reveal? State in plain language as if yu were explaining t a friend wh knws very little statistics H2Ot emp 15. What is yur best guess fr the crrelatin cefficient between water temperature and fish activity. 16. If we reversed the variables and made a scatterplt f fish activity vs. water temperature, what wuld the new crrelatin cefficient be? Briefly explain yur reasning. 3

4 17. Suppse we were t recrd temperature in Celsius degrees instead f Fahrenheit. Hw wuld the crrelatin change? Why? 18. Suppse a new pint at (84, 300), i.e., water temperature = 84 F and fish activity = 300, is added t the plt. Describe the effect, if any, that this new pint will have n the crrelatin cefficient f water temperature vs. fish activity and hw it will affect the slpe f the line. Why des it have this effect? The table shws the number f live births per 1000 wmen aged years in the United States starting in When yu enter the data, enter year as 65, 70, 75, 80, 85, etc.: YEAR Rate Which is the explanatry variable? 20. Make a scatterplt f the data by hand. 21. Determine the equatin f the LSRL fr this data using yur TI-84. Define yur variables: 22. Plt the line n yur scatterplt. Plt it n yur TI-84 and then just cpy it frm the screen. 23. What is the slpe? Define the slpe in the cntext f this prblem. 24. What is the crrelatin between x and y? Interpret this value in the cntext f this prblem. 25. What is the cefficient f determinatin? Interpret this number. 4

5 26. Predict what the birth rate will be in Cmment n yur faith in this predictin. 27. Find the residual fr the first pint in the data set. Shw yur wrk belw fr credit. 28. Cnstruct a residual plt in yur calculatr and sketch it belw. 29. Use the residual plt t answer this questin: Is a linear mdel apprpriate fr these tw variables? Explain. A cnsumer rganizatin has reprted test data fr 50 car mdels. We will examine the assciatin between the weight f the car (in thusands f punds) and the fuel efficiency (in miles per galln). Predictr Cef StDev T P Cnstant Weight S = R-Sq = 75.6% R-Sq(adj) = 71.2% 30. Using the printut abve, find the LSRL Find the crrelatin between weight f a car and its gas mileage What is yur estimate f fuel efficiency (MPG) fr a car that weighs 3000 lbs? Review: The number f new prjects started each mnth at an advertising agency fr the last six mnths is: The interquartile range fr the abve data is (A) 1.0 (B) 2.0 (C) 3.0 (D) 4.0 (E)

6 34. The weight f a randmly selected can f a new sft drink is knwn t have a nrmal distributin with a mean f 8.3 unces and a standard deviatin f 0.2 unces. The weight that shuld be stamped n each can s that nly 2% f all cans are underweight is (A) 7.89 unces. (B) 8.13 unces. (C) 8.26 unces. (D) 8.71 unces. (E) 8.02 unces Birth weights at a lcal hspital have a nrmal distributin with a mean f 110 unces and a standard deviatin f 15 unces. The prprtin f infants with birth weights under 95 unces is (A) (B) (C) (D) (E)

TEST 3A AP Statistics Name: Directions: Work on these sheets. A standard normal table is attached.

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