Question

A wild-life biologist believes the sex ratio of badgers deviates from the expected 1 : 1
male to female ratio in a particular forest and predicts there is an excess of males.
In a random sample they obtain: 10 males and 2 females.
Conduct the most appropriate statistical test.

Use bionomial test, and please show detailed calculations.

Answer 1

Solution:

Binomial Test

Null hypothesis: H₀: The sex ratio of badgers is 1:1.

Alternative hypothesis: H_a: The sex ratio of badgers is not 1:1.

We are given n=10+2 = 12

If sex ratio is same, then p = 0.5

We have n=12, p = 0.5

We are given X = 10 males out of n = 12.

P(X=x) = nCx*p^x*(1 – p)^(n – x)

P(X=10) = 12C10*0.5^10*(1 – 0.5)^(12 – 10)

P(X=10) = 12C10*0.5^10*0.5^2

P(X=10) = 66* 0.000977* 0.25

P(X=10) = 0.016121

Our binomial test indicates that the probability of getting 10 males out of total 12 subjects is given as 0.016121 which differs than the ideal value of 0.5. So, we reject the null hypothesis.

There is sufficient evidence to conclude that the sex ratio of badgers deviates from the expected 1 : 1 male to female ratio in a particular forest.