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A poll of 1130 teens aged 13 to 17 showed that $53 \%$ of them have made new friends online. Use a 0.01 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. $$\begin{array}{l|l} \mathrm{H}_{0}: \mathrm{p} & \mathbf{Y} \\ \mathrm{H}_{1}: \mathrm{p} & \mathbf{Y} \\ \square \end{array}$$ (Type integers or decimals. Do not round.)