Question

According to a genetic model, the distribution of fur color of the second generation Havana rabbit (Oryctolagus cuniculus) should be 1:2:1, black:gray:brown. In a sample of second generation rabbits, there are 10 black, 27 gray, and 16 brown rabbits. Assuming random sample and independent observations, does this sample of rabbits suggest that the actual fur color distribution differs from the genetic model? Include all steps for full credit.

Answer 1

Here we want to test "does this sample of rabbits suggest that the actual fur color distribution differs from the genetic model?"

For this we need to use goodness of fit test.

Let's write null and the alternative hypothesis.

H₀ :  the actual fur color distribution is same as the genetic model.

H₁ :  the actual fur color distribution is different from the genetic model.

The formula of test statistic as follow

Where O is the observed frequencies

E = expected frequencies.

Let's make table in excel:

If the level of significance is not given then consider it as 0.05 ( 5%)

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.5022 > 0.05 so we used 2nd rule.

That is we fail to reject null hypothesis

Conclusion: At 5% level of significance there are not sufficient evidence to say that the actual fur color distribution is different from the genetic model.