4. Probability theory and the binomial expansion (see Investigation 3) show that
ID: 199978 • Letter: 4
Question
4. Probability theory and the binomial expansion (see Investigation 3) show that, were you to sample families consisting of four children, 1/16 of these families would consist of 4 boys, 4/16 would consist of 3 boys and I girl, 6/16 would consist of 2 boys and 2 girls, 4/16 would consist of 1 boy and 3 girls, and I/16 would consist of 4 girls. Do the data in the sample given in the next table approximate this expectation? Complete the table, calculate X', and answer the questions based on your calculations. (O-E)VE Family Sex Ratio (O-E) (O-E)Explanation / Answer
Null hypothesis: The observed values are not deviating from the expected values.
Test static:
Category
All boys
3B 1G
2B 2G
1G 3B
All girls
Total
Observed values
235
898
1317
841
181
3472
Exptected Ratio
1
4
6
4
1
16
Exprected Values
217
868
1302
868
217
3472
Deviation
18
30
15
-27
-36
D^2
324
900
225
729
1296
D^2/E
1.493088
1.036866
0.172811
0.839862
5.97235
9.514977
X^2
9.514977
Degrees of freedom
5-1=4
Inference: The calcuclated chisquare value i.e. 9.51 is greater than the table value i.e. 9.49 at 4 DF and 0.05 probability. Hence the null hypothesis is rejected.
A. The degrees of freedom = No of chategories - 1 = 5-1 = 4.
B. Rejected the hypothesis because the calcuted chisuqare values is greater than the table value.
C. The answer is Xero.
D. Find the below chisquare test
Category
All boys
3B 1G
2B 2G
1G 3B
All girls
Total
Observed values
235
898
1317
841
181
3472
Exptected Ratio
1
4
6
4
1
16
Exprected Values
217
868
1302
868
217
3472
Deviation
18
30
15
-27
-36
D^2
324
900
225
729
1296
D^2/E
1.493088
1.036866
0.172811
0.839862
5.97235
9.514977
X^2
9.514977
Degrees of freedom
5-1=4
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