Question

In 2010 polls indicated that 75% 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 2010?

We test the hypothesis that the percentage supporting mandatory testing is less than 75% this year The p-value is 0.013
Which of the following interpretation of this p-value is valid?
A. The probability that Americans have changed their opinion on this issue since 2010 is 0.013.
B. There is a 1.3% chance that the null hypothesis is true.
C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.

Answer 1

C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.

Explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 1000 Americans is under test. It is the result of the poll that 75% still favor mandatory testing.