Question

In 2001 polls indicated that 74% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2001? We test the hypothesis that the percentage supporting mandatory testing is less than 74% this year. The P-value is 0.015. Which of the following interpretation of this P-value is valid? Group of answer choices There is a 1.5% chance that the null hypothesis is true. The probability that Americans have changed their opinion on this issue since 2001 is 0.015. If 74% of Americans still favor mandatory testing this year, then there is a 1.5% chance that poll results will show 71% or fewer with this opinion.

Answer 1

The right answer is:

"If 74% of Americans still favor mandatory testing this year, then there is a 1.5% chance that poll results will show 71% or fewer with this opinion."

Explanation:

The P-value represents the probability of getting the sample we got, given that the null hypothesis is true. For this reason, it the P-value is lower than the significance level, it means that the sample result is unlikely due to chance, but due to a false null hypothesis.

In this case, the P-value represents a probability P=0.015 of having a sample with proportion p=0.71, given that the population has a proportion π=0.74.

The right answer is:

"If 74% of Americans still favor mandatory testing this year, then there is a 1.5% chance that poll results will show 71% or fewer with this opinion."