Question

Mendelian Genetics Experiments are conducted with hybrids of two types of peas. If the offspring follow Mendel's theory of inheritance, the seeds that are produced are yellow smooth, green smooth, yellow wrinkled, and green wrinkled, and they should occur in the ratio of 9:3:3:1, respectively. An experiment is designed to test Mendel's theory, with the result that the offspring seeds consist of 307 that are yellow smooth, 77 that are green smooth, 98 that are yellow wrinkled, and 18 that are green wrinkled. Use a 0.05 significance level to test the claim that the results contradict Mendel's theory.

a) χ^2 test statistic
b) Degree of freedom
c) Critical value at 0.05 significance level
d) Conclusion based on the test

Answer 1

To test the claim that the results of the experiment contradict Mendel's theory, a chi-squared test can be used. The test compares observed frequencies with expected frequencies to determine significance and utilizes a critical value. The conclusions based on the test depend on the calculated chi-squared value and the critical value.

Step-by-step explanation:

To test the claim that the results of the experiment contradict Mendel's theory of inheritance, a chi-squared test can be utilized. The chi-squared test statistic is calculated by comparing the observed frequencies (307, 77, 98, 18) with the expected frequencies (9/16, 3/16, 3/16, 1/16) and determining the significance of the differences. The degree of freedom for this test is 3, as there are 4 categories. The critical value at a 0.05 significance level with 3 degrees of freedom is approximately 7.815.

By comparing the calculated chi-squared test statistic value with the critical value, it can be determined whether the results contradict Mendel's theory. If the calculated value is greater than the critical value, it would indicate significant deviation from the expected ratios and suggest that the experiment results contradict Mendel's theory. Alternatively, if the calculated value is less than or equal to the critical value, there is insufficient evidence to reject Mendel's theory.