Question

< Chapter 2 hmk part 2 Problem 2.31 6 of 10 In a sample of families with 6 children each, the distribution of boys and girls is as shown in the following table: Number of famaes 9 | 6 | 147 204 | 15 Number of boys Part A Calculate the chi-square value to test the hypothesis of a boy-to-girl ratio of 1:1 Express your answer using three decimal places. Request Answer ▼ Part B Are the numbers of boys to girls in these families consistent with the expected 1:1 ratio? O no O yes Request Answer Part C Calculate the chi-square value to test the hypothesis of binominal distribution in six-child families. Express your answer using three decimal places. Request Answer Part D Is the distribution of the numbers of boys and girls in the families consistent with the expectations of binomial probability? O ye

Answer 1

Answer:

Based on the given data:

Number of families	9	63	147	204	151	56	10
Number of girls	0	1	2	3	4	5	6
Number of boys	6	5	4	3	2	1	0

Total number of boys = 9*6 + 63*5 + 147*4 + 204*3 + 151*2 + 56*1 + 10*0 = 1927

Total number of girls = 9*0 + 63*1 + 147*2 + 204*3 + 151*4 + 56*5 + 10*6 = 1913

Total number of child = 1927 + 1913 = 3840

	Observed Number (O)	Expected Number (1:1) (E)	(O-E)	(O-E)^2/E
Boys	1927	3840/2 = 1920	-7	0.026
Girls	1913	3840/2 = 1920	7	0.026
			Sum (Chi Square)	0.051

Chi square value = 0.051

Degree of freedom = number of categories - 1 = 1

Probability value corresponding to a chi square value of 0.051 with 1 degree of freedom is P-Value = 0.821332. The result is not significant at p < 0.05.

Part A:Calculate the chi-square value to test the hypothesis of a boy-to-girl ratio of 1:1 Express your answer using three decimal places.

• Chi square value = 0.051

Part B Are the numbers of boys to girls in these families consistent with the expected 1:1 ratio?

• Yes