A sample of 120 families with 4 children each in which both parents are carriers
ID: 313349 • Letter: A
Question
A sample of 120 families with 4 children each in which both parents are carriers of an autosomal recessive mutation for cystic fibrosis (CF)produces the following distribution of children with and without cystic fibrosis:
Part A
Calculate the chi-square value to test the hypothesis that CF is inherited as an autosomal recessive trait.
(Recall that the chi-square formula is (O-E)2/E, where O is the observed number of offspring in each outcome class, E is the number of expected for each class and the summation, , is taken over all possible outcome classes.)
Express your answer as an integer.
Part B
What is the expected ratio of families with 0 through 4 children with CF in this sample under the assumptions of binomial probability?
Express your answer as five numbers (each to three decimal places), separated by colons.
0 : 1 : 2 : 3 : 4 children with CF = ?
These are the only info I have from Mastering Genetics
Number of families 16 52 32 18 2 Children with CF 0 1 2 3 4 Children free of CF 4 3 2 1 0Explanation / Answer
Both parents are carriers of the trait. So, expected ratio is 3:1.
Null hypothesis: Ho: The inheritance pattern is Mendelian; and independent assortment occurs. CF is inherited as an autosomal recessive trait.
Alternate hypothesis H1: The inheritance pattern is not Mendelian. CF is not inherited as an autosomal recessive trait.
120 families with four children each is there. 120*4 = 480 children were born. This means that out of 480, 360 should be normal, and 120 should be affected.
Observed
Expected
(O-E)^2/E
Having the disease
10
360
-350^2/360 = 340.3
Free of CF
10
120
-110^2/120 = 100.8
Total
441.1
Calculated value = 441.1 (Answer to Part A)
Degree of freedom = (3-1) (3-1) = 4
Tabulated value = 9.49
Null hypothesis is accepted if calculated value is less than tabulated value.
Level of significance = 0.05
Here, calculated value is more than the tabulated value; so, null hypothesis is rejected. CF is not inherited as an autosomal recessive trait.
Part B
Expected ratio in Mendelian fashion is 3:1 (always).
** For binomial probability please post in Maths.
Observed
Expected
(O-E)^2/E
Having the disease
10
360
-350^2/360 = 340.3
Free of CF
10
120
-110^2/120 = 100.8
Total
441.1