Many teens have posted profiles on sites such as Facebook. A sample survey asked random samples of teens with online profiles if they included false information in their profiles. Of 170 younger teens (ages 12 to 14) polled, 117 said “Yes.” Of 317 older teens (ages 15 to 17) polled, 152 said “Yes.”7 A 95% confidence interval for p_Y − p_O = the true difference in the proportions of younger teens and older teens who include false information in their profile is 0.120 to 0.297.

a. Interpret the confidence interval.

b. Does the confidence interval give convincing evidence of a difference in the true proportions of younger and older teens who include false information in their profiles? Explain your answer.