Question

A paper reported that in a representative sample of 286 American teens age 16 to 17, there were 77 who indicated that they had sent a text message while driving. For purposes of this exercise, assume that this sample is a random sample of 16- to 17-year-old Americans. Do these data provide convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving? Test the appropriate hypotheses using a significance level of 0.01. (Round your test statistic to two decimal places and your P-value to four decimal places.)

State your conclusion:

a. Reject H0. We do not have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.
b. Do not reject H0. We have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.
c. Do not reject H0. We do not have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.
d. Reject H0. We have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.

Answer 1

c. Do not reject H0. We do not have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.

Explanation:

First let's divide the number if teens that indicates that they texted.

77/286= 0.2692

This fraction is up to quarter of the total teens but not the quarter population of the American.

But with the population of the American teens ,from 16 to 17 more than quarter, there is a high probability that the entire teens and signifying that the number of the population texting might be up to quarter.