Problem # 2: Data from adoption studies on handedness indicate that the effects

Question

Problem # 2: Data from adoption studies on handedness indicate that the effects of shared biological heritage are more powerful determinants of hand preference than sociocultural factors. Biological offspring were found to show nonrandom distributions of right and non-right handedness as a function of parental handedness. In contrast, the handedness distribution of adopted children as a function of parental handedness was essentially random The following table gives the handedness of biological offspring as a function of parental handedness. gical Offs Parental Hand Right-Handed Left-Handed father mother Riaht x Left (a) Find the values in cells (2,2) and (3,2) of the expected table. (b) Can a chi-square analysis be performed on the above table? (c) Combine the last two rows in the above table to create a new 2 x 2 table. (The meaning of the 2nd row in this new table would be "at least one of the parents is left-handed.) If we use the resulting 2 x 2 table to test the hypothesis that the handedness of the biological offspring is independent of the handedness ofthe parents using the 1% significance level, that is teralue ofthe test tatistic? (d) Find the critical value for the test in (c) (e) What is the conclusion? expacted value (correct t 3 declmals Problem 20a) (A) No, because the population is not normal. (B) Yes, because all of the observed frequencies are at least 5. (C) Yes, because only some of the expected frequencies are less than 5. (D) Yes, because at least one of the expected frequencies is less than 5 (E) Yes, because at least one of the observed frequencies is less than 5 (F) No, because at least one of the expected frequencies is less than 5. (G) No, because at least one of the observed frequencies is less than 5. Problem #2(b): I select Problem #2(c) test setac (carrect to 2 declmals critical value (correct to 3 declmals) (A) We conclude that the factors are dependent since the anstwer in (c is less than or equal to the answer in (d) (B) We conclude that the factors are independent since the answer in (c) is less than or equal to the answer in (d) (C) Reject the hypothesis of independence since the answer in (c) is greater than the answer in (d) (D)Reject the hypothesis of independence since the answer in (c) is less than or equal to the answer in (d) (E) We conclude that the factors are independent since the answer in ( is greater than the answer in (d) ? Do not reject the hypothesis of independence since the answer in ( is greater than or equal to the answer in (d) (G) Do not reject the hypothesis of independence since the answer in (c) is less than or equal to the answer in (d) Problem #2(e): I seect concusion

Explanation / Answer

a) expecte value =(row total*column total)/grand total =4.940 ; 4.550

b) option F

c)

test statistic =4.50

d) critical value =6.635

e) option G

Observed Oi right handed left handed Total right*right 290 37 327 right*left 58 15 73 Total 348 52 400 Expected Ei=?row*?column/?total right handed left handed Total right*right 284.490 42.510 327 right*left 63.510 9.490 73 Total 348 52 400 chi square =(Oi-Ei)2/Ei right handed left handed Total right*right 0.1067 0.7142 0.821 right*left 0.4780 3.1992 3.677 Total 0.585 3.913 4.498

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