Question

In 2010 polls indicated that 73% 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 72% 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 73% 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 73% of Americans still favor mandatory testing this year, then there is a 1% chance that poll results will show 72% or fewer with this opinion.

Answer 1

Option A is correct.

The probability that Americans have changed their opinion on this issue since 2010 is 0.013.

Explanation:

In Hypothesis testing, the p-value is the probability of obtaining results as extreme as the observed results if the null hypothesis is true.

The null hypothesis plays the devil's advocate and is always about the absence of significant difference between two variables being compared.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared.

The p-value is the probability of obtaining extreme result, that is, that there has been a significant difference in the samples being compared if the null hypothesis were true.

And for this question, the extreme result translates to a significant change in opinion on the issue since 2010.

Hence, a p-value of 0.013 indicates that the probability of obtaining the result that Americans have changed their opinion on this issue since 2010 is 0.013 given that the null hypothesis (that they haven't changed their mind) is true.

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