Probability theory and the binomial expansion show that were you to sample famil

Question

Probability theory and the binomial expansion show that were you to sample families consisting of four children, 1/16th of these families can be expected to consist of 4 boys, 4/16th would consist of 3 boys and 1 girl, 6/16ths would consist of 2 boys and 2 girls, 4/16ths would consist of 1 boy and 3 girls, and 1/16th would consist of 4 girls. Does the data in the sample given below approximate this expectation? Calculate chi-squared, and answer the questions below.

Family Sex Ratio

Observed

All boys

175

3B:1G

657

2B:2G

924

1B:3G

572

All girls

137

-How many degrees of freedom does chi-squared analysis have?

-In this case, do you accept or reject the null hypothesis?

-What is the probability that the deviations are due to chance alone?

Family Sex Ratio

Observed

All boys

175

3B:1G

657

2B:2G

924

1B:3G

572

All girls

137

Explanation / Answer

degrees of freedom does chi-squared analysis have =n-1=5-1=4

for above at 0.05 level critical value =9.4877

as test stat 10.6073 is higher then 9.4877, we reject null hypothesis.

probability that the deviations are due to chance alone=p value =0.0314

observed Expected Chi square X Probability O E=total*p =(O-E)^2/E all boys 1/16 175.000 154.06 2.85 3B:1G 1/4 657.000 616.25 2.69 2B:2G 3/8 924.000 924.38 0.00 1B:3G 1/4 572.000 616.25 3.18 All girls 1/16 137.000 154.06 1.89 1 2465 2465 10.6073

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