Soc 3811 Basic Social Statistics Third Midterm Exam Spring 2010

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1 Soc 3811 Basc Socal Statstcs Thrd Mdterm Exam Sprng 2010 Your Name [50 ponts]: ID #: Your TA: Kyungmn Baek Meghan Zacher Frank Zhang INSTRUCTIONS: (A) Wrte your name on the lne at top front of every sheet. (B) If you use a page of notes n takng ths exam, sgn & nsert t nsde ths booklet before turnng n your exam. (C) Show your calculatons for numercal problems n the space provded! Usng a random sample of 436 Vetnamese rce farmers, an agronomst regresses the number of bushels harvested per acre (Y) on pounds of fertlzer per acre (X), resultng n ths predcton equaton (the standard errors are n parentheses): X R 2 YX (17.4) (1.2) Use her equaton to estmate how many bushels of rce were harvested by farmers usng these amounts of fertlzer [5 ponts]: X

2 2. Calculate the coeffcents of determnaton (R 2 ) for three dfferent regresson equatons wth these sums of squares and numbers of ndependent varables [5 ponts]: (1): Four ndependent varables SS ERROR = 18,271 SS TOTAL = 24,482 R2 = (2): Eght ndependent varables SS REGRESSION = 759 SS ERROR = 3,824 R2 = (3): Three ndependent varables SS REGRESSION = 4,263 SS TOTAL = 8,327 R2 =

3 Your name: 3. Test a famly socologst s research hypothess that more years of educaton a mother has (X), the fewer the fghts among her chldren (Y). Ths bvarate regresson equaton used a sample of 438 mothers wth two chldren between ages 6 to 12 years (the standard errors are n parentheses): 48.7 (8.2) 1.4 X (0.6) R 2 YX Wrte hs null and research hypotheses about β YX n symbolc form; show your calculatons of the test statstc; state your decson about H 0 and the lowest probablty of Type I (false rejecton) error. State the substantve concluson of your decson. (See the crtcal values tables on page 11 of ths exam.) [5 ponts]: H0: H1: Decson about H0: Probablty of Type I error: State the substantve concluson of your decson:

4 4. Now test the null hypothess about the coeffcent of determnaton from the bvarate regresson n the precedng problem. Wrte the null and research hypotheses n symbolc form; show your calculatons of the test statstc n the ANOVA table; state your decson about H 0 and the lowest probablty of Type I error. State the substantve concluson of your decson. (Crtcal-values table s on page 11). [5 ponts]: H0: H1: Source SS df MS F Regresson 791 Error 16,409 Total 17, Decson about H0: Probablty of Type I error: State the substantve concluson of your decson:

5 Your name: 5. A poltcal scentst analyzes congressonal electons by regressng the vote for Republcan canddates on eght ndependent varables n a sample of 215 electoral dstrcts. Her estmated R 2 = Show your computaton of R 2 adj.. [5 ponts]: R 2 adj.

6 6. An economst hypotheszes that unemployment n the Great Recesson can be explaned by sx corporate varables. She regresses a measure of job layoffs on those sx ndependent varables for a sample of 215 corporatons, producng the ANOVA table below. Wrte her null and research hypotheses about the coeffcent of determnaton n symbolc form; complete the analyss of varance table; state your decson about H 0 ; gve the lowest probablty of Type I error; and state your substantve concluson. [5 ponts]: H0: H1: Source SS df MS F Regresson 556 Error 9,457 Total 10, Decson about H0: Probablty of Type I error: State the substantve concluson of your decson:

7 Your name: 7. A real estate researcher hypotheszes that both house and neghborhood factors affect home prces. For a sample of 547 homes, he frst regresses home prce on sx house varables and fnds a coeffcent of determnaton R 2 = After addng four neghborhood ndependent varables to the equaton, the second equaton R 2 = Wrte the researcher s null and alternatve hypotheses n symbolc notaton; carry out the approprate statstcal test; state your decson about H 0 ; and, f you reject H 0, report the lowest probablty of Type I error. [5 ponts]: H0: H1: Decson about H0: Probablty of Type I error: State the substantve concluson of your decson:

8 8. Usng data from a sample of 673 released felons, a crmnologst regresses a measure of recdvsm (Y) on educaton (X 1 ), hours worked (X 2 ), and age (X 3 ), producng ths unstandardzed predcton equaton: X X 0.19 X (5.36) (0.09) (0.14) (0.04) 2 3 R 2 adj Use the standard devatons below to change the unstandardzed b s n the equaton above nto standardzed coeffcents (β*). Then wrte the standardzed regresson equaton and dentfy the strongest predctor of recdvsm. [5 ponts]: VARIABLE Recdvsm (Y) 6.0 Educaton (X1) 4.0 Employment (X2) 8.0 Age (X3) 15.0 STD. DEV. Standardzed Eq.: Strongest predctor:

9 Your name: 9. A Mnnesota hstoran uses 28,472 Census records from 1890 to study how educaton (Y ) vared among European mmgrant groups. The nonordered varable ETHNIC has fve categores (below). Show the codng scheme to change ETHNIC nto a set of dummy varables for use as ndependent varables n a multple regresson equaton. [5 ponts]: ETHNIC 1. Swedsh 2. Norwegan 3. German 4. Irsh 5. Other Use ths regresson equaton to estmate the educaton of mmgrants wth each ethncty: D Swedsh 0.8 D Norwegan 1.5 D German 1.2 D Irsh R 2 adj Swedsh Norwegan German Irsh Other

10 10. A relgon scholar regresses the frequency of prayer on: a 10-pont relgosty measure (X RELIG ); age (X AGE ), coded n years; and a race dummy varable (D RACE ), coded 1 = nonwhte, 0 = whte. The unstandardzed and standardzed ANCOVA equatons are: X RELIG 0.3 X AGE 4.7 D RACE R 2 adj Ẑ Y 0.5 Z RELIG 0.3 Z AGE 0.2 Z RACE Calculate the predcted frequency of prayer for: (a) A 20 year old nonwhte person of low relgosty (X RELIG = 2): (b) A 70 year old whte person of hgh relgosty (X RELIG = 8): Wrte a bref substantve nterpretaton of how the three predctors each affect frequency of prayer, and ndcate whch predctor(s) has the largest effect:

11 Crtcal values (c.v.) of Z and t for large samples One-tal c.v. Two-tal c.v Crtcal values (c.v.) of F dstrbutons for large samples df R, df E =.05 =.01 =.001 1, , , , , , , , , ,

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