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Make sure to use R In an experiment in breeding mice, a geneticist has obtained 120...


In an experiment in breeding mice, a geneticist has obtained 120 brown mice with pink eyes, 48 brown mice with brown eyes, 36
Make sure to use R

In an experiment in breeding mice, a geneticist has obtained 120 brown mice with pink eyes, 48 brown mice with brown eyes, 36 white mice with pink eyes and 13 white mice with brown eyes. Theory predicts that these types of mice should be obtained in the ratios 9:3:3 : 1. Test the compatibility of the data with theory, using a 5% critical value. 1. What are the null and alternate hypotheses? 2. What is the p-value of you test? Show the R code and the outputs. 3. What is your conclusion? Why?
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Answer #1

Sol:

expected percentages are

9/9+3+3+1=9/16=0.5625

3/16=0.1875

3/16=0.1875

1/16= 0.0625

Solution-1:

Ho:fo=fe

observed frequencies and expected frequencies are same

Ha: fo not =fe

observed frequencies differs from expected frequencies

Solution-2:

Rcode:

observedeyes <- c(120,48,36,13)
expectedeyes <- c(0.5625,0.1875,0.1875,0.0625)
chisq.test(observedeyes, p=expectedeyes)

Output:

Chi-squared test for given probabilities

data: observedeyes
X-squared = 1.9124, df = 3, p-value = 0.5908

p value= 0.5908

Solution-3:

p value= 0.5908

p>0.05

Do not reject Ho

Accept Ho

Conclusion:

There is sufficient evidence at 5% level of significance to conclude that data is compatible with the theory

as obseved frequencies are same as expected frequencies

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