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. Parental Handedness (father x mother) Right x Right Right x Left Left & Right Biological Offspring Right-Handed 299 29 21 Left-Handed 37 8 6 (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 × 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 × 2 table to test the hypothesis that the handedness of the biological offspring is independent of the handedness of the parents using the 1% 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?

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Chapter1: Starting With Matlab
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I got (a) half right I got (b) and (e) wrong 

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.
Parental Handedness
(father x mother)
Problem #2(a): 4.717, 3.442
Right x Right
Right x Left
Left & Right
Biological Offspring
Right-Handed
299
29
21
(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 × 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 × 2 table to test the hypothesis that the handedness of
the biological offspring is independent of the handedness of the parents using
the 1% 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?
Left-Handed
37
8
6
expected values (correct to 3 decimals)
separate your answers with a comma
(A) Yes, because only some of the expected frequencies are less than 5.
(B) No, because at least one of the expected frequencies is less than 5.
(C) No, because the population is not normal.
Transcribed Image Text: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. Parental Handedness (father x mother) Problem #2(a): 4.717, 3.442 Right x Right Right x Left Left & Right Biological Offspring Right-Handed 299 29 21 (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 × 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 × 2 table to test the hypothesis that the handedness of the biological offspring is independent of the handedness of the parents using the 1% 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? Left-Handed 37 8 6 expected values (correct to 3 decimals) separate your answers with a comma (A) Yes, because only some of the expected frequencies are less than 5. (B) No, because at least one of the expected frequencies is less than 5. (C) No, because the population is not normal.
Problem #2(a): 4.717, 3.442
(A) Yes, because only some of the expected frequencies are less than 5.
(B) No, because at least one of the expected frequencies is less than 5.
(C) No, because the population is not normal.
(D) Yes, because at least one of the observed frequencies is less than 5.
(E) Yes, because at least one of the expected frequencies is less than 5.
(F) No, because at least one of the observed frequencies is less than 5.
(G) Yes, because all of the observed frequencies are at least 5.
Problem #2(b): G
Problem #2(c): 5.70
Problem #2(d): 6.635
expected values (correct to 3 decimals)
separate your answers with a comma
test statistic (correct to 2 decimals)
(A) Reject the hypothesis of independence since
the answer in (c) is less than or equal to the answer in (d)
critical value (correct to 3 decimals)
(B) Do not reject the hypothesis of independence 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) We conclude that the factors are independent since
the answer in (c) is greater than the answer in (d)
(E) Do not reject the hypothesis of independence since
the answer in (c) is greater than or equal to the answer in (d)
Problem #2(e): D
(F) We conclude that the factors are independent since
the answer in (c) is less than or equal to the answer in (d)
conclusion
(G) We conclude that the factors are dependent since
the answer in (c) is less than or equal to the answer in (d)
Transcribed Image Text:Problem #2(a): 4.717, 3.442 (A) Yes, because only some of the expected frequencies are less than 5. (B) No, because at least one of the expected frequencies is less than 5. (C) No, because the population is not normal. (D) Yes, because at least one of the observed frequencies is less than 5. (E) Yes, because at least one of the expected frequencies is less than 5. (F) No, because at least one of the observed frequencies is less than 5. (G) Yes, because all of the observed frequencies are at least 5. Problem #2(b): G Problem #2(c): 5.70 Problem #2(d): 6.635 expected values (correct to 3 decimals) separate your answers with a comma test statistic (correct to 2 decimals) (A) Reject the hypothesis of independence since the answer in (c) is less than or equal to the answer in (d) critical value (correct to 3 decimals) (B) Do not reject the hypothesis of independence 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) We conclude that the factors are independent since the answer in (c) is greater than the answer in (d) (E) Do not reject the hypothesis of independence since the answer in (c) is greater than or equal to the answer in (d) Problem #2(e): D (F) We conclude that the factors are independent since the answer in (c) is less than or equal to the answer in (d) conclusion (G) We conclude that the factors are dependent since the answer in (c) is less than or equal to the answer in (d)
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