When we are conducting a two-tailed hypothesis test for a proportion, if the test statistic $Z=1.15$, what is the P-value? (Round your answer to 3 decimal places.) Question Help: B Read Post to forum

Step 1 ：In a two-tailed hypothesis test, we are interested in deviations in both directions from the hypothesized value. Therefore, we need to find the probability of observing a Z-score of 1.15 or more, or -1.15 or less. This is equivalent to finding the area under the standard normal curve to the right of 1.15 and to the left of -1.15.

Step 2 ：To find this, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives us the probability that a random variable is less than or equal to a certain value. Therefore, to find the probability that the Z-score is greater than 1.15, we need to subtract the CDF at 1.15 from 1.

Step 3 ：Since this is a two-tailed test, we need to multiply this probability by 2 to account for the other tail of the distribution.

Step 4 ：By performing these calculations, we find that the P-value is 0.25.

Step 5 ：Final Answer: The P-value for a two-tailed hypothesis test with a test statistic of \(Z=1.15\) is \(\boxed{0.25}\).