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

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 Biological Offspring Right-HandedLeft-Handed Parental HandednessR (father x mother) Right x Right Right Left Left × Right 306 29 16 37 (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 2x 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 of the parents using the 5% significance level, what is the value of the test statistic? (d) Find the critical value for the test in (c) (e) What is the conclusion? expected values (correct to 3 decimals) separate your answers with a comma Problem #2(a): (A) Yes, because at least one of the observed frequencies is less than 5 (B) Yes, because at least one of the expected frequencies is less than 5 (C) No, because the population is not normal. (D) Yes, because all of the observed frequencies are at least 5 (E) Yes, because only some of the expected frequencies are less than 5 (F) No, because at least one of the observed frequencies is less than 5 (G) No, because at least one of the expected frequencies is less than 5 Problem #2(b): Select B Problem #2(c): test statistic (correct to 2 decimals) Problem #2(d): critical value (correct to 3 decimals) (A) Do not reject the hypothesis of independence since the answer in (c) is greater than or equal to the answer in (d) (B) Reject the hypothesis of independence since the answer in (c) is less than or equal to the answer in (d) (C) Do not reject the hypothesis of independence since the answer in (c) is less than or equal to the answer in (d) (D) We conclude that the factors are dependent since (E) We conclude that the factors are independent since the answer in (c) is less than or equal to the answer in (d) the answer in (c) is greater than the answer in (d) (F) Reject the hypothesis of independence since (G) We conclude that the factors are independent since the answer in (c) is greater than the answer in (d) the answer in (c) is less than or equal to the answer in (d)

Explanation / Answer

expected value is (2.2) cell =row total *colulmn total/grand total =4.29

expected value is (3.2) cell =row total *colulmn total/grand total =2.7

2a) expected values =4.29 ; 2.7

2b) option G

2c)applying chi square goodness of fit test:

test statistic =4.79

2d) critical value =3.841

2e)option F

Observed Oi right handed left handed Total right*right 306 37 343 right*left 45 12 57 Total 351 49 400 Expected Ei=?row*?column/?total right handed left handed Total right*right 300.983 42.018 343 right*left 50.018 6.98 57 Total 351 49 400 chi square =(Oi-Ei)2/Ei right handed left handed Total right*right 0.0836 0.5992 0.683 right*left 0.5033 3.6055 4.109 Total 0.587 4.205 4.792

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