Question

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. 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 x Right Biological Offspring Right-Handed Left-Handed 294 137 30 (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? Problem #2(a): expected values (correct to 3 decimals) separate your answers with a comma (A) Yes, because all of the observed frequencies are at least 5. (B) Yes, because only some of the expected frequencies are less than 5. (C) No, because at least one of the expected frequencies is less than 5. (D) No, because the population is not normal. (E) Yes, because at least one of the expected frequencies is less than 5. (F) Yes, because at least one of the observed frequencies is less than 5. (G) No, because at least one of the observed frequencies is less than 5.

Answer 1

a) 3.878, 4.230

b)

(C) No, because at least one of the expected frequencies is less than 5.

c)

Expected	Ei=row total*column total/grand total	R-H	L-H	Total
	R-R	292.108	38.893	331
	R-L	60.893	8.108	69
	total	353	47	400
chi square    χ2	=(Oi-Ei)2/Ei	R-H	L-H	Total
	R-R	0.0123	0.0921	0.1043
	R-L	0.0588	0.4418	0.5006
	total	0.0711	0.5338	0.6049
test statistic X2 =		0.60

for 1 df and 0.1 level of signifcance critical value χ2=

2.706

(B) Do not reject the hypothesis of independence since the answer in (c) is less than or equal to the answer in (d)