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 p1 = 0.25, p2 = 0.50, and p3 = 0.25. A random sample of 200 plants yields X2 = 4.88. (a) Carry out a test of the null hypothesis that the theory is correct, using level of significance α = 0.05. (Use technology. Round your answer to four decimal places.) P-value = State the conclusion in the problem context. Fail to reject H0. There is convincing evidence that the researcher's theory is incorrect. Reject H0. There is not convincing evidence that the researcher's theory is incorrect. Fail to reject H0. There is not convincing evidence that the researcher's theory is incorrect. Reject H0. There is 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 X2. How would your analysis and conclusion differ from those in part (a)? 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 analysis and conclusion would not change. 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.

please also eaplain how do you calculate the number expected

Answer 1

(a) Carry out a test of the null hypothesis that the theory is correct, using level of significance α = 0.05. (Use technology. Round your answer to four decimal places.) P-value = 0.0872

State the conclusion in the problem context.

Fail to reject H0. 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 X2. How would your analysis and conclusion differ from those in part (a)?

The analysis and conclusion would not change.

Irrespective of the numbers, the statistic takes into consideration only the number of classes(in this case 3) and hence, the degrees of freedom for is the same in both the instances.

please also explain how do you calculate the number expected

The expected values(frequencies) are obtained by multiplying the total by the Hypothesized proportions.

For example, when the number of plants are 200, the expected counts will be for the first phenotype=200*0.25=50,For the second phenotype it is 200*0.5=100 and for the third it is 200*0.25=50.