A sample of 120 families with 4 children each in which both

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

Solution

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.