Question

As part of the Pew Internet and American Life Project, researchers surveyed a random sample of $800$teens and a separate random sample of $400$young adults. The teens, $79\%$said that they own an iPod or MP3 player. For the young adults, this figure was$67\%$. Is there a significant difference between the population proportions? State appropriate hypotheses for a significance test to answer this question. Define any parameters you use

Short answer

$H_0:p_1-p_2=0$

$H_a:p_1-p_2\ne 0$

Step-by-step solution

Given Information

Given

${\hat{p}}_1=79\%=0.79$

$n_1=800$

${\hat{p}}_2=67\%=0.67$

$n_2=400$

Explanation

The null hypothesis states that the population proportions are equal or that their difference is zero:

$H_0:p_1-p_2=0$

The alternative hypothesis states the opposite of the null hypothesis (according to the claim):

$H_a:p_1-p_2\ne 0$

$p_1$is the population proportion of teens that own an iPod or MP3 player.

$p_2$is the population proportion of young adults that own an iPod or MP3 player.