You are conducting a study to see if the probability of catching the flu this year is significantly different from $51 \%$. With $H_{1}: p \neq 51 \%$ you obtain a test statistic of $z=2.469$. Find the $p$-value accurate to 4 decimal places.
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p \text {-value }=
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Step 1 ：We are conducting a study to see if the probability of catching the flu this year is significantly different from 51%. The alternative hypothesis is \(H_{1}: p \neq 51 \%\).

Step 2 ：We obtain a test statistic of \(z=2.469\).

Step 3 ：The p-value is the probability that a random chance generated the data, or something else that is equal or rarer. In this case, we are looking for the probability that we would observe a test statistic as extreme as \(z=2.469\) under the null hypothesis that the true population proportion is 51%.

Step 4 ：Since the alternative hypothesis is two-sided (\(p \neq 51%\)), we need to find the two-tailed p-value. This means we will find the probability that a z-score is less than -2.469 or greater than 2.469 under the standard normal distribution.

Step 5 ：After calculation, we find that the p-value is 0.013549121846580737.

Step 6 ：We simplify this to 4 decimal places to get the final answer.

Step 7 ：The final answer is: \(\boxed{0.0135}\).