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Answer :
(a) To test the compatibility of data with theory in the breeding mice experiment, we can use the chi-square goodness-of-fit test.
The null hypothesis (H0) is that the observed frequencies are consistent with the expected frequencies based on the theory. The alternative hypothesis (Ha) is that there is a significant difference between the observed and expected frequencies.
The expected frequencies can be calculated by multiplying the total number of mice by the respective genetic percentages. In this case, the expected frequencies are:
Expected frequencies for brown mice with pink eyes: (120+48+36+13) * 0.56 = 150
Expected frequencies for brown mice with brown eyes: (120+48+36+13) * 0.19 = 50
Expected frequencies for white mice with pink eyes: (120+48+36+13) * 0.19 = 50
Expected frequencies for white mice with brown eyes: (120+48+36+13) * 0.06 = 16
Now we can calculate the chi-square test statistic:
χ^2 = Σ((Observed frequency - Expected frequency)^2 / Expected frequency)
Using the given observed frequencies and the calculated expected frequencies, we can calculate the chi-square test statistic. If the test statistic is greater than the critical value from the chi-square distribution table at the chosen level of significance (0.05), we reject the null hypothesis.
(b) To test the homogeneity of repair distribution among the three shops, we can use the chi-square test of independence.
The null hypothesis (H0) is that there is no association between the shop and the type of repair. The alternative hypothesis (Ha) is that there is an association between the shop and the type of repair.
We can construct an observed frequency table based on the given data:
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| Shop 1 | Shop 2 | Shop 3 | Total
Complete | - | 78 | 56 | 134
Adjustment | - | 15 | 30 | 45
Incomplete | - | 7 | 14 | 21
Total | 100 | 100 | 100 | 200
To perform the chi-square test of independence, we calculate the expected frequencies under the assumption of independence. We can calculate the expected frequencies by multiplying the row total and column total for each cell and dividing by the overall total.
Once we have the observed and expected frequencies, we can calculate the chi-square test statistic:
χ^2 = Σ((Observed frequency - Expected frequency)^2 / Expected frequency)
If the test statistic is greater than the critical value from the chi-square distribution table at the chosen level of significance (0.05), we reject the null hypothesis.
Learn more about frequencies here -: brainly.com/question/254161
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