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 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. There is a 1.5% chance that the null hypothesis is true.

Answer 1

The correct option is option 2.

Explanation:

In this case we need to test whether the previous data for the proportion of Americans who favored mandatory testing of students in public schools as a way to rate the school has decreased this year or not.

The hypothesis can be defined as follows:

H₀: The proportion supporting mandatory testing is not less than 74% this year, i.e. p ≥ 0.74.

Hₐ: The proportion supporting mandatory testing is less than 74% this year, i.e. p < 0.74.

It is provided that the p-value of the test is,

p-value = 0.015

The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

The p-value of 0.015 or 1.5% implies that, if it is true that 74% of Americans still favor mandatory testing this year, then the probability that the poll results will show that 71% or less with the same opinion is 1.5%.

Thus, the correct option is option 2.