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 hypothesied proportions are P, -0.25, P2 - 0.50, and P, -0.25. A random sample of 200 plants yields - 4.72 (a) Carry out a test of the hull hypothesis that the theory is correct, using level of significance - 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 contest 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. Fail to reject There is not convincing evidence that the researcher's theory is incorrect. Reject H. 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 previous analysis yielded a significant result and the null hypothesis was rejected. The new analysis w not yield a gricant result and the null hypothesis would fail to be rejected The analysis and conclusion would not change The previous analyses did not yield a significant result and then ypothesis and to be rejected. The new analysis wu yield a nd cant result and the full hypothes would be rejected

Answer 1

here, n =200

number of categories (k) = 3

degrees of freedom = (k-1) = (3-1) = 2

critical value be = 5.99

[ for df = 2, alpha= 0.05, from chi square table ]

the conclusion be:-

fail to reject H₀ . there is not convincing evidence that the researcher's theory is incorrect.

[ as,chi square calculated = 4.72 < 5.99

so, we fail to reject the null hypothesis. ]

b).the analysis and conclusion would not change.

[ because, now n = 300 and the chi square statistic has the same value as before.

the critical value of chi square does not depend on n ...so it will remain unchanged...and so our conclusion. ]

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