Question

In a sample of families with 6 children each, the distribution of boys and girls is as shown in the following table:

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	0

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

Answer 1

Part A & C

First Set of 10 Families	Female	Male	Total
Observed No (o)	0	6	6
Expected No (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, the value should come 3.851 to be significant
But our value is larger than this, so it is insignificant and hence hypothesis of a boy-to-girl ratio of 1:1 is Fail
First Set of 60 Families	Female	Male	Total
Observed No (o)	1	5	6
Expected No (E)	3	3	6
O-E	-2	2	0
(O-E)2	4	4	0
(O-E)2/E	1.666	1.6663	x2=3.332
Our value lies in the range so, the hypothesis can be accepted.
First Set of 147 Families	Female	Male	Total
Observed No (o)	3	3	6
Expected No (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, the value should come near by 0.456 is acceptable
This Data is 50% we can say more significant and nearby to accept the hypothesis
First Set of 202 Families	Female	Male	Total
Observed No (o)	2	4	6
Expected No (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, the value should come nearby 0 to be acceptable.
This data is more significant and close to accept the hypothesis i.e., 99.5%.
First Set of 148 Families	Female	Male	Total
Observed No (o)	4	2	6
Expected No (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
Same Data Is availanle for the next two calculations also so theirfore values will be the same
First Set of 62 Families	Female	Male	Total
Observed No (o)	5	1	6
Expected No (E)	3	3	6
O-E	2	-2	0
(O-E)2	4	4	0
(O-E)2/E	1.666	1.666	x2=3.332
First Set of 10 Families	Female	Male	Total
Observed No (o)	6	0	6
Expected No (E)	3	3	6
O-E	3	3	0
(O-E)2	9	9	0
(O-E)2/E	3	3	x2=6

Part B : No the consistence ratio of boys and girls are not 1:1

Part D :No