How big is your family? The General Social Survey asked a sample of 2780 adults

Question

How big is your family? The General Social Survey asked a sample of 2780 adults how many children they had, and also how many siblings (brothers and sisters) they had. The results are summarized in the following contingency table. Number of Children Siblings 0 1 2 3 4 More than 4 54 15 33 22 14 1 192 100 169 65 25 16 171 102 136 77 33 28 81 132 85 28 30 88 56 85 64 3218 More than 4 121 128 180 161 76 50 Send data to Exce (a) Compute the expected frequencies. (b) Compute the value of the test statistic (c) How many degrees of freedom are there? (d) Test the hypothesis of independence. Use the a-0.1 level of significance. What do you conclude?

Explanation / Answer

a) here as expected frequency =row total*column total/grand total

expected value table is as follows:

b)

applying chi square tst:

test statsitic =128.2869

c)

degree of freedom =(row-1)*(column-1)=(6-1)*(6-1)=25

d)

here for 0.10 elvel and 25 degree of freedom critical value =34.382

as test statsitic is higher than critical value we reject null hypotheiss

and conclude that number of sibligns one have is related to number of children the person has,

Expected Ei=?row*?column/?total 0 1 2 3 4 more than 4 0 38.785 24.794 37.808 24.382 10.699 6.533 1 153.783 98.307 149.908 96.676 42.423 25.903 2 148.901 95.186 145.149 93.606 41.076 25.080 3 125.305 80.102 122.147 78.773 34.567 21.106 4 93.029 59.470 90.685 58.483 25.663 15.669 more than 4 194.196 124.141 189.302 122.081 53.571 32.709

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