1. Soc2205a/b Final Review

2. Healey 1e 8.2, 2/3e 7.2 Problem information:  = 3.3 = 3.8 s =.53 n = 117 Use the 5-step method…. Note: –1 sample, Interval-ratio –Sample is large n ≥ 100 z-test –Question asks “Is there a significant difference?” 2-tailed test

3. Step 4: Calculations

4. Step 5: Interpretation α =.05 Z cr = ± 1.96 Reject H o Sociology majors are significantly different (Z=10.16, α =.05)

5. Healey 1e 8.11, 2/3e 7.11 Problem information: Pu =.10 Ps =.14 N = 527 Use the 5-step method…. Note for Steps 1 - 3: –1 sample, Nominal –Sample is large n ≥ 100 z-test –Question asks “Are older people more likely…?” 1-tailed test (Note: question says do a 2 tailed test also)

6. Step 4: Calculations

7. Step 5: Interpretation α =.05 Z cr = +1.65 (for 1-tailed) Reject H o Older people are more likely to be victimized. (Z=3.06, α =.05)

8. Healey 1e 9.3a, 2/3e 8.3a Problem information: Hockey Football = 460 = 442 s 1 = 92 s 2 = 57 n 1 = 102n 2 = 117 Use the 5-step method…. Note: –2 samples, Interval-ratio –Sample is large n ≥ 100 z-test –Question asks “Is there a significant difference?” 2-tailed test

9. Step 4: Calculations

10. Step 4: Calculations (cont.) Z

11. Step 5: Interpretation α =.05 Z cr = ± 1.96 Fail to reject H o Hockey players are not significantly different from football players. What if the question had asked “Do hockey players have a higher aptitude score…?” Try conducting the significance test again!

12. Healey 1e 9.12a, 2/3e 8.12a Problem information: Special Regular P s1 =.53P s2 =.59 n 1 = 78 n 2 = 82 Use the 5-step method…. Use the 5 step method… Note: –2 samples, Nominal –Sample is large n ≥100 z-test –Question asks “Did the new program work? (i.e. is it better” 1-tailed test

13. Step 4: Calculations

14. Step 4: Calculations (cont.) Z

15. Step 5: Interpretation α =.05 Z cr = - 1.65 Fail to reject H o The new program did not work.

16. Healey 1e 10.8a, 2/3e 9.8a Problem information: –Occupational Prestige Scores for 3 Groups (Urban, Suburban, Rural) Use the 5 step method… Note: –3 samples, Interval-ratio F-test, One-way ANOVA –Question asks “Are there differences by place of residence (Urban, Suburban, Rural) – dfw = N - k = 30 - 3 = 27 – dfb = k - 1 = 3 - 1 = 2 – F cr = 3.35

17. Step 4: Make Computational Table Grand Mean= (include n-sizes too) UrbanSuburbanRural ∑X i ∑X 2 Group Means

18. Step 4: Calculations (cont.)

19. SSW = SST - SSB SSW = 3590 – 825.8 SSW = 2764.2

20. Step 4: Calculations (cont.) Within estimate (MSW) Between estimate (MSB) F = Between estimate (MSB) / within estimate (MSW) = 412.9 / 102.38 = 4.03

21. Step 5: Interpretation α =.05 F cr = 3.32 Reject H o At least one of the groups (urban, suburban, rural) is significantly different. (F = 4.03, df = 2, 27, α =.05)

22. Healey 1e 11.5, 2/3e 10.5 Problem information: SalaryUnionNon-unionTotal High212950 Low143650 Total3565 100 Is there a relationship? Answer the 3 questions… Use the 5 step method for hypothesis test. Note: Tabular Data, Nominal x Ordinal –Df= (rows-1 x columns-1) = 1 –α=.05, X 2 cr = 3.841

23. Step 4: Expected Frequencies Top left cell: Top right cell: Bottom left cell: Bottom right cell:

24. Step 4: Computational Table f o f e f o –f e (f o - f e ) 2 (f o - f e ) 2 /f e 21 17.50 3.50 12.25 0.70 29 32.50 -3.50 12.25 0.38 14 17.50 -3.50 12.25 0.70 36 32.50 3.50 12.25 0.38 N=100 0.00 χ 2 (obt.) = 2.16

25. % and Strength of Association SalaryUnionNon-union High60%44.6% Low40%55.4% Total 100%100% Max. difference: 15.4% Strength: Phi = Weak association.

26. Step 5: Decision and Interpretation Fail to reject H o There is no significant relationship between salary levels and unionization. Three questions: –Association?Not significant –Strength?Weak, Phi =.147 –Pattern?Union members more likely to make high salary while non-union more likely to make low salary.

27. Healey 1e 14.8, 2/3e 12.8 Problem information:Authoritarianism Depression Low Moderate HighTotal Few 7 8 9 24 Some 15 10 18 43 Many 8 12 3 23 Total 30 30 30 90 Is there a relationship? Answer the 3 questions… Note: Tabular Data, Ordinal x Ordinal, Gamma Use the 5 step method for hypothesis test. –α=.05, Z cr = ±1.96

28. Step 4: Calculations N s :7 (10+18+12+3) = 7 (43) = 301 8 (18+3) = 8 (21) = 168 15 (12+3) = 15 (15) = 225 10 (3) = 30 Total N s = 724 N d : 9 (15+10+8+12) = 9 (45) = 405 8 (15+8) = 8 (23) = 184 18 (8+12) = 18 (20) = 360 10 (8) = 80 Total N d = 1029

29. Step 4: Calculations (cont.) There is a weak, negative relationship between parenting style and depression. Z obt <Z crit. Fail to reject H o. The association is not significant (Note: Hypothesis test. Use 5 step model)

30. Step 5 Interpretation Answering the 3 questions…. Association?Not significant Strength?Weak, G = -.174 Pattern/Direction?Negative, parents who are higher in authoritarianism have children with fewer depression symptoms.* –*calculate % also.

31. Healey 1e 15.3, 2/3e 13.3 Is there a relationship? –Draw scattergram –Find r and r 2 –Find regression line –Calculate predicted visitors for activity = 5 and 18 Answer the 3 questions… Note: Interval-ratio data, regression and correlation Use the 5 step method for hypothesis test… –α=.05, df=n-2, t cr = ±2.306 Problem information: CaseActivity Visitors X Y A10 14 B11 12 C12 10 D10 9 E15 8 F9 7 G7 10 H3 15 I10 12 J9 2

32. Scattergram Y=a+bX

33. Make A Computational Table Case X YX 2 Y 2 XY A1014 B1112 C1210 D109 E158 F97 G710 H315 I1012 J92 TotalsΣXΣYΣX 2 ΣY 2 ΣXY

34. Totals of Computational Table  X= 96  Y= 99  X²= 1010  Y²= 1107  XY= 918 9.6 9.9

35. Slope (b) * 3 decimals b = -.367

36. Y-intercept (a)

37. Pearson’s r * 3 decimals r = -.306

38. Coefficient of Determination (r 2 ) and Hypothesis (t) test Coefficient of Determination: r 2 = (r) 2 = (-.306) 2 =.094 9.4% of variation in visitors is explained by activity level Hypothesis test: Fail to reject H o (t obs = -.91 < t cr = ±2.306)

39. Predictions* for Activity Level For X = 5 –Ŷ = a + bX = 13.42 + (-.367)(5) = 11.6 visitors For X = 18 –Ŷ = a + bX = 13.42 + (-.367)(18) = 6.8 visitors *use the calculated prediction values to draw actual regression line on the scattergram

40. Summary r = -.306 r 2 =.094 There is a weak, negative relationship between # of visitors and activity levels for seniors. As activity levels go down, # of visitors increases. The relationship is not significant. Activity levels explain 9.4% of the variation in # of visitors.