Chapter 11.2, Problem 57E

To determine

To explain: The correct interpretation in which the statistic $x^2=69.8$ and the p value tends to 0.

Answer to Problem 57E

The correct answer is Option (b).

Explanation of Solution

Given information:

Software gives test statistic ${\chi }^2=69.8$ and P value close to 0

The p-value in hypothesis testing is the probability of obtaining a test statistic value at least as extreme as the observed value, when the null hypothesis is assumed to be true.

The p-value is the probability of obtaining a value (statistic) of the test result as extreme as, or more extreme than, the value that has been obtained, assuming H₀ to be true. So, the p-value is not considered in making the probability. It is just a probability of getting a certain result when H₀ is true.

In the given scenario, the interpretation of the result is:

The probability of obtaining a test statistic value χ² = 69.8 at least as extreme as the observed value, when the null hypothesis is assumed to be true is 0.

That is, the probability of getting a random sample of 4877 teens that yields a value of χ² of 69.8 or larger if H₀ is true is basically true.

Therefore, the correct answer is Option (b).