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. Biological Offspring Parental Handedness (father × mother) Right-Handed Left-Handed Right × Right 298 37 Right × Left 29 6 Left × Right 24 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?
Problem #2(a):	expected values (correct to 3 decimals) separate your answers with a comma
	(A) Yes, because at least one of the expected frequencies is less than 5. (B) Yes, because at least one of the observed frequencies is 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 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) Yes, because all of the observed frequencies are at least 5.

Answer 1

Parental Handedness	Right-Handed	Left-Handed	Total
Right × Right	298	37	335
Right × Left	29	6	35
Left × Right	24	6	30
Total	351	49	400

a) Expected value for (2, 2) = 49 * 35 / 400 = 4.288

Expected value for (2, 3) = 49 * 30 / 400 = 3.675

---

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

---

c)

Parental Handedness	Right-Handed	Left-Handed	Total
Right × Right	298	37	335
at least one is left-handed	53	12	65
Total	351	49	400
Expected Frequencies
	Right-Handed	Left-Handed	Total
Right × Right	351 * 335 / 400 = 293.9625	49 * 335 / 400 = 41.0375	335
at least one is left-handed	351 * 65 / 400 = 57.0375	49 * 65 / 400 = 7.9625	65
Total	351	49	400
	(fo-fe)²/fe
Right × Right	(298 - 293.9625)²/293.9625 = 0.0555	(37 - 41.0375)²/41.0375 = 0.3972
Right × Left	(53 - 57.0375)²/57.0375 = 0.2858	(12 - 7.9625)²/7.9625 = 2.0473

Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 2.7858

---

d) df = (r-1)(c-1) = 1

Critical value:

χ²α = CHISQ.INV.RT(0.01, 1) = 6.6349

---

e) Decision:

Do not reject the null hypothesis.