Question

N a test population of 1000 people, 210 display hemophilia. you hypothesize that this trait follows mendelian genetics with a 3:1 ratio of non- hemophilia to hemophilia. use the χ2 test to determine whether the data support the hypothesis or not. show your steps and explain your reasoning.

Answer 1

According to the 3:1 ratio, you expect, out of a population of 1000 people, 750 non-hemophilia and 250 hemophilia.

The chi-square value can be calculated by the formula:
$\chi^{2} = \frac{(O - E)^{2}}{E}$

where:
O = observed value = 210
E = expected value = 250

Therefore:
χ² = (210 - 250)² / 250
    = 6.4

Now, look at a χ² distribution table, in order to find the p-value. In this case, you have only 1 degree of freedom and the closest χ² is 6.6 which corresponds to a p-value of 0.01.

Since p < 0.05, which is the minimum value generally accepted, we can say that the data do not support the hypothesis.