According to a genetic model, the distribution of fur color of the second genera

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 8 black, 24 gray, and 17 brown rabbits.

a. What statistical test do they need to run to determine if these rabbits match the expected ratio? (1 pt)

b. What are the null and alternative hypothesis for this test? (2 pts)

c. Find your test statistic. (5 pts)

d. What is your critical value? (1 pt)

e. What is your conclusion? (1 pt)

Explanation / Answer

A.Chi square test for sample proportion is needed to run to determine if these rabbits match the expected ratio.

b.Null hypothesis: The proportion of black, gray and brown are is 25%(1/(1+2+1)*100%), 50% and 25% respectively.

The alternative hypothesis is: At least one of the proportions in the null hypothesis is false.

c.The degrees of freedom=k-1=3-1=2

Now expected value is Ei=n*pi

E1=49*0.25=12.25

E2=49*0.50=24.5

E3=49*0.25=12.25

The test statistic chi square is:

Sum over(Oi-Ei)^2/Ei

=(8-12.25)^2/12.25+(24-24.5)^2/24.5+(17-12.25)^2/12.25

=3.32

d.The critical value is: chi square(2,0.05)=5.991

e.The test statistic does not fal lin the critical region. Thus fail to reject the null hypothesis.

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