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 Parental HandednessR Right-Handed Left-Handed (father x mother) Right x Right Right x Left Left x Right 307 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 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 of the parents using the 10% 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) No, because the population is not normal (C) Yes, because only some of the expected frequencies are less than 5 (D) No, because at least one of the observed frequencies is less than 5 (E) Yes, because all of the observed frequencies are at least 5 (F) No, because at least one of the expected frequencies is less than 5 (G) Yes, because at least one of the expected frequencies is less than 5 Problem #2(b): | Select ? 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) We conclude that the factors are independent since (C) 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) (D) Reject the hypothesis of independence 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) We conclude that the factors are dependent since (G) Do not reject the hypothesis of independence since the answer in (c) is less than or equal to the answer in (d) the answer in (c) is less than or equal to the answer in (d) (E) Reject the hypothesis of independence since

Explanation / Answer

applying chi square test:

2a) as exected values =(row total*column total)/grand total

hence correct answers are 4.080 , 2.640

2b) option E

2c) test statisitic =5.60

2d) critical value =4.605

2e)

option E

Observed Oi right handed left handed Total rightxright 307 37 344 rightxleft 29 5 34 leftxright 16 6 22 Total 352 48 400 Expected Ei=?row*?column/?total right handed left handed Total rightxright 302.720 41.280 344 rightxleft 29.920 4.080 34 leftxright 19.360 2.640 22 Total 352 48 400 chi square =(Oi-Ei)2/Ei right handed left handed Total rightxright 0.0605 0.4438 0.504 rightxleft 0.0283 0.2075 0.236 leftxright 0.5831 4.2764 4.860 Total 0.672 4.928 5.600

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