Software gives test statistic ${\chi }^2=69.8$and $P$-value close to 0 . The correct interpretation of this result is

(a) the probability of getting a random sample of $4877$teens that yields a value of ${\chi }^2$of $69.8$or larger is basically $0$.

(b) the probability of getting a random sample of $4877$teens that yields a value of ${\chi }^2$of $69.8$or larger if $H_0$is true is basically $0$.

(c) the probability of making a Type I error is basically $0$.

(d) the probability of making a Type II error is basically $0$.

(e) it's very unlikely that these data are true.

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

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 ${\mathrm{H}}_0$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 ${\mathrm{H}}_0$is true.

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

The probability of obtaining a test statistic value $X^2=69.8$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 localid="1650450318348" $x^2$of localid="1650450326474" $69.8$or larger iflocalid="1650450369804" ${\mathrm{H}}_0$is true is basically true.

Therefore, the correct answer is Option (b).