A gene comes in 2 forms, a short form and a long form. In the population, 20% of people have at least one copy of the short form of the gene. Researchers believe that the short form of the gene is linked to having diabetes. They want to test their theory that more than 20% of all diabetics have at least one copy of the short form of the gene. To test their theory, they randomly selected 100 diabetics and have them tested for the short form of the gene. They find that 26 of the subjects in their study have at least one copy of the short form of the gene, for a p-value of 0.0668. The probability we would reject the null hypothesis, if in reality the population proportion were 0.26, is 0.0668. The probability we would find a sample proportion of 0.2 or greater, if in reality the population proportion were 0.26, is 0.0668. The probability we would reject the null hypothesis, if in reality the population proportion were 0.2, is 0.0668. The probability we would find a sample proportion of 0.26 or greater, if in reality the population proportion were 0.2, is 0.0668.Are the assumptions met for the hypotheses above? (which one is correct?)

a. Yes, since (100)(0.2) = 20 > 15, and the diabetics are randomly selected.
b. Yes, since (100)(0.26) = 26 > 15, and the diabetics are randomly selected.
c. Yes, since (100)(0.74) = 74 > 15, and the diabetics are randomly selected.
d. Yes, since (100)(0.2) = 20 > 10, and the diabetics are randomly selected.
e. Yes, since (100)(0.8) = 80 > 10, and the diabetics are randomly selected.

Which of the following sample proportions would have given even more evidence than the sample proportion we found in favor of the researchers' claim that more than 20% of all diabetics have at least one copy of the short form of the gene?

a.0.02
b.0.29
c.0.20
d.0.23
e.0.16
Calculate the p-value for this study. Round your answer to three decimal places.