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.
$h_0:p = 0.5$
$h_1:p
eq0.5$
(type integers or decimals. do not round)
identify the test statistic
$z = 3.36$
(round to two decimal places as needed)
identify the p - value
p - value $=0.001$
(round to three decimal places as needed)
state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim
$square$ the null hypothesis. there $square$ sufficient evidence to $square$ the claim that half of all teens have made new friends online

Explanation:

Step1: Compare P - value and significance level

We are given a significance level \(\alpha = 0.05\) and a P - value \(P=0.001\).
Since \(P = 0.001<\alpha=0.05\)

Step2: Make a decision about the null hypothesis

When \(P<\alpha\), we reject the null hypothesis \(H_0\).

Step3: State the conclusion about the claim

Since we reject \(H_0:p = 0.5\), there is sufficient evidence to support the claim that the proportion of teens who have made new friends online is not \(0.5\) (i.e., to reject the claim that half of all teens have made new friends online)

Answer:

Reject the null hypothesis. There is sufficient evidence to reject the claim that half of all teens have made new friends online.