According to a genetic model, the distribution of fur color of the second genera
ID: 3135529 • Letter: A
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. What statistical test do they need to run to determine if these rabbits match the expected ratio? What are the null and alternative hypotheses for this test? Find your test statistic, show the rejection region for the test, and make a decision using the rejection region. What is your p-value? What decision would you make using the p-value? What is your conclusion?Explanation / Answer
A)
It is a chi-squared goodness-of-fit test.
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b)
Ho: The distribution of fur color of the second generation Havana rabbit is 1:2:1, black:gray:brown.
Ho: The distribution of fur color of the second generation Havana rabbit is not 1:2:1, black:gray:brown.
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c)
Doing an observed/expected value table,
O E (O - E)^2/E
8 12.25 1.474489796
24 24.5 0.010204082
17 12.25 1.841836735
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 3.326530612 [ANSWER, TEST STATISTIC]
As df = a - 1,
a = 3
df = a - 1 = 2
Then, the critical chi^2 value is
significance level = 0.05
chi^2(crit) = 5.991464547
Hence, reject Ho when chi^2 > 5.991. [ANSWER, REJECTION REGION]
Hence, as chi^2 = 3.327 < 5.991, WE FAIL TO REJECT THE NULL HYPOTHESIS. [ANSWER, DECISION]
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d)
Also, the p value is
p = 0.189519131 [ANSWER]
As P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
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e)
Thus, there is no significant evidence that the distribution of fur color of the second generation Havana rabbit is not 1:2:1, black:gray:brown at 0.05 level. [CONCLUSION]
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