Chapter 8, Problem 99CRE

Texting While Driving The mother of a teenager has heard a claim that $25\%$ of teenagers who drive and use a cell phone reported texting while driving. She thinks that this rate is too high and wants to test the hypothesis that fewer than $25\%$ of these drivers have texted while driving. Her alternative hypothesis is that the percentage of teenagers who have texted when driving is less than $25\%.$

${\text{H}}_{\text{0}}:p=0.25$

${\text{H}}_{\text{a}}:p<0.25$

She polls 40 randomly selected teenagers, and 5 of them report having texted while driving, a proportion of $\mathrm{0.125.}$ The p-value is $\mathrm{0.034.}$ Explain the meaning of the p-value in the context of this question.