A certain genetic characteristic of a particular plant can appear in one of thre

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 = .25, p2 = .50, and p3 = .25. A random sample of 200 plants yields 2 = 5.28.

(a) Carry out a test of the null hypothesis that the theory is correct, using level of significance = .05. (Round your answer to three decimal places.)

P-value =

(b) Suppose that a random sample of 300 plants had resulted in the same value of 2.

How would your analysis and conclusion differ from those in Part (a)?

1.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.

2.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.

3.The analysis and conclusions would not change.

Explanation / Answer

chi sq, X2 = 5.28

When sample size is 200 , degrees of freedom = 200 - 1 = 199

p value of chi square for 5.28 with 199 degrees of freedom from chi square table = 7.000841e-117

Since significance level is 0.05, the corresponding X2 value is 167.361. Hence we accept the null hypothesis as actual X2 value is less than critical X2 value. Hence we accept the theory is correct that the proportions are p1 = .25, p2 = .50, and p3 = .25.

b. At sample size 300 , p value for 5.28 chi square value is 1.669e-200.

Critical chi square value at 0.05 significance level is 259.945.

Hence we again accept the null hyothesis.

3.The analysis and conclusions would not change.

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