A genetic theory says that a cross between two pink flowering plants will produce red flowering plants a proportion p = 0.25 of the time. To test the theory, 100 crosses are made and 31 of them produce a red flowering plant. Is this evidence that the theory is wrong?
What is the P-value for this significance test?
A) 0.0808
B) 0.1616
C) 0.5000
D) 0.9192

Question

Quizplus · Accepted Answer

We can use a binomial distribution with n=100 and p=0.25 to calculate the probability of getting at least 31 red flowering plants by chance alone. Using a calculator or software, we find the p-value to be approximately 0.1616. This is not a very small value, so we do not have strong evidence to reject the theory. Alternatively, we can use a one-tailed test with a significance level of 0.05, and compare the observed proportion (31/100=0.31) to the expected proportion (0.25) using a z-test. The test statistic is z = (0.31 - 0.25) / sqrt(0.25*0.75/100) = 1.4. The critical value for a one-tailed test at alpha=0.05 is 1.645. Since 1.4 < 1.645, we do not reject the theory. Therefore, the answer is B.

A Genetic Theory Says That a Cross Between Two Pink