Question

a poll of 1132 teens aged 13 to 17 showed that 55% of them have made new friends online. use a 0.05 significance level to test the claim that half of all teens have made new friends online. use the p - value method. use the normal distribution as an approximation to the binomial distribution
let p denote the population proportion of all teens aged 13 to 17 who have made new friends online. identify the null and alternative hypotheses
$h_0$ p
$h_1$ p
(type integers or decimals. do not round)

Explanation:

Step1: Set up the null hypothesis

The claim is that half of all teens have made new friends online. So the null hypothesis \(H_0\) is \(p = 0.5\) (since half is \(0.5\)).

Step2: Set up the alternative hypothesis

The poll shows \(55\%\) (\(0.55\)) of teens have made new friends online. We are testing against the claim of half (\(0.5\)). Since \(0.55>0.5\), the alternative hypothesis \(H_1\) is \(p> 0.5\) (a right - tailed test).

Answer:

\(H_0:p = 0.5\)
\(H_1:p>0.5\)