Question

A certain genetic characteristic of a particular plant can appear in one of three forms (phenotypes). A researcher has developed a theory, according to which the hypothesized proportions are p = 0.25, P, = 0.50, and p = 0.25. A random sample of 200 plants yields x2 = 5.27. (a) Carry out a test of the null hypothesis that the theory is correct, using level of significance a = 0.05. What is the critical value for the test? (Round your answer to two decimal places.) Critical Value = State the conclusion in the problem context. Fail to reject Ho. There is not convincing evidence that the researcher's theory is incorrect. Reject H. There is convincing evidence that the researcher's theory is incorrect. Fail to reject Ho. There is convincing evidence that the researcher's theory is incorrect. Reject Ho. There is not convincing evidence that the researcher's theory is incorrect. (b) Suppose that a random sample of 300 plants had resulted in the same value of x. How would your analysis and conclusion differ from those in part (a)? The analysis and conclusion would not change. The previous analysis did not yield a significant result and the null hypothesis failed to be rejected. The new analysis would yield a significant result and the null hypothesis would be rejected. The previous analysis yielded a significant result and the null hypothesis was rejected. The new analysis would not yield a significant result and the null hypothesis would fail to be rejected.

Answer 1

a) Degrees of freedom = 3 - 1 = 2

So,

Critical value at 0.05 significance level = 5.99

Conclusion: Option A is correct.

b) Option A is correct.