. How do you ac ount 10! llI Binomial expansion tells us that in families of fiv
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. How do you ac ount 10! llI Binomial expansion tells us that in families of five children, you may expect 1/32 of the families to consist entirely of boys, 5/32 to consist of 4 boys and 1 girl, 10/32 to consist of 3 boys and 2 girls, 10/32 to consist of 2 boys and 3 girls, 5h2 to consist of 1 boy and 4 girls, and 1/32 to consist entirely of girls. Do the datan such families of five children given in the following table approximate the distribu tion suggested? Complete the table, calculate X', and answer the related questions 6. Family Sex Ratio (0-E)" (0-E)2/E 0 61 280 525 494 231 41 O-E All boys 48: 1G 3B: 2G 2B: 3G 1B: 4G All girls TotalsExplanation / Answer
a) There are 6 different sex ratios in the familes.The degree of freedom is number of different sex ratio minus 1 . Therefore degree of freedom is 5
b) Our chi square values 0.956 lies between 0.975 and 0.95 probability values. We can take the average of these probability values. 0.975 + 0.95 /2 = 0.96, Therefore there is 96% probability of observing the sex ratio as mentioned in the table. This value is greater than the 5% (0.05) significance level. If P value is greater than or equal to 5% then we accept the hypothesis and if P value is less than 5% we reject the hypothesis.Therefore we accept the hypothesis
c) The probability that the deviation observed are due to chance alone is 96% .
d) The total number of children are 5 x 867= 4335 , where 867 is the total number of families.
63 families have all boys, 284 families have 4 boys and 520 families have 3 boys. The total number of boys is 63 x 5 + 284 x 4 + 520 x 3 = 3011.
284 families have 1 girl and 520 families have 2 girls. The total number of girls is 284 x 1 + 520 x 2 = 1324
If there is a 50:50 sex ratio the expected number of boys will be 50/100 x 4335 = 2167.5 and expected number of girls will also be 50/100 x 4335 = 2167.5.
e. We reject the hypothesis that sex ratio is 50:50 as our calculated chi-square value is very high and has a probability (P) values much less than 0.005. This P values is much less than 0.5 significance value.
Degree of freedom is 1 as the number of classes is 2 (male and female) and 2-1 =1
f. Ratio of boys to girls : Number of boys is 3011 and number of girls is 1324. The ratio is 3011/1324 = 2.27/1 i.e. 2.27 : 1
Family sex ratio O E O-E (O-E)2 (O-E)2 /E all boys 61 1/32 x 1632= 51 10 100 1.96 4B:1G 280 5/32 x 1632 = 255 25 625 2.45 3B:2G 525 10/32 x 1632 = 510 15 225 0.44 2B:3G 494 10/32 x 1632 = 510 -16 256 0.5 1B:4G 231 5/32 x 1632 = 255 -24 576 2.25 all girls 41 1/32 x 1632 = 51 -10 100 1.96 Total = 1632 families chi square = sum of all (O-E)2 /E values = 9.56Related Questions
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