In a sample of families with 6 children each, the distribution of boys and girls
ID: 189244 • Letter: I
Question
In a sample of families with 6 children each, the distribution of boys and girls is as shown in the following table:
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)
Part B) Are the numbers of boys to girls in these families consistent with the expected 1:1 ratio? Yes or No
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)
Part D) Is the distribution of the numbers of boys and girls in the families consistent with the expectations of binomial probability? Yes or No
Number offamilies 10 60 147 202 148 62 10 Number of girls 0 1 2 3 4 5 6 Number of boys 6 5 4 3 2 1 0Explanation / Answer
First set of 10 families
Female
Male
Total
Observed numbers (O)
0
6
6
Expected numbers (E)
3
3
6
O - E
0-3 = -3
3
0
(O-E)2
9
9
0
(O-E)2 / E
3
3
X2= 6
in chi square table at p = 0.05, at degree of freedon(n-1) = 1, the value should be 3.841 to be significant
But our value is larger than this, so it is insignificant and hence trhe hypothesis that ratio of 1:1 boys and girls is rejected
First set of 60 families
Female
Male
Total
Observed numbers (O)
1
5
6
Expected numbers (E)
3
3
6
O - E
-2
2
0
(O-E)2
4
4
0
(O-E)2 / E
1.666
1.6663.331
X2= 3.332
in chi square table at p = 0.05, at degree of freedon(n-1) = 1, the value should be 3.841 to be significant. Our value lies in the range so, the hypothesis can be accepted.
First set of 147 families
Female
Male
Total
Observed numbers (O)
3
3
6
Expected numbers (E)
3
3
6
O - E
0
0
0
(O-E)2
0
0
0
(O-E)2 / E
0
0
X2= 0
in chi square table at p = 0.5, at degree of freedon(n-1) = 1, the value should be 0.455 to be significant. This data is more significant and close to accept the hypothesis i.e., 50%
First set of 202 families
Female
Male
Total
Observed numbers (O)
2
4
6
Expected numbers (E)
3
3
6
O - E
-1
1
0
(O-E)2
1
1
0
(O-E)2 / E
0.333
0.333
X2= 0.666
in chi square table at p = 0.995, at degree of freedon(n-1) = 1, the value should be 0 to be significant. This data is more significant and close to accept the hypothesis i.e., 99.5%.
This data is more significant than any other.
For next three cases same procedure will be followed, as there is same data in families with 148,62 and 10 families.
The result of 148 will be equal to that of 147, 62 will be equal to that of 60 no. families data and 10 will be equal to 10.
B. The result says that the numbers of boys to girls in these families are not consistent with the expected 1:1 ratio.
First set of 10 families
Female
Male
Total
Observed numbers (O)
0
6
6
Expected numbers (E)
3
3
6
O - E
0-3 = -3
3
0
(O-E)2
9
9
0
(O-E)2 / E
3
3
X2= 6
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