A one-sample Z-test with a 2-tailed alternative hypothesis was carried out.A z-statistic of 2.35 has been calculated for the sample mean.Find the P-value, correct to three decimal places.

To find the P-value for a one-sample Z-test with a 2-tailed alternative hypothesis and a z-statistic of 2.35, follow these steps:

1. Understand the Z-statistic: The Z-statistic is 2.35. This value represents the number of standard deviations the sample mean is away from the population mean under the null hypothesis.

2. Determine the P-value for a 2-tailed test: For a 2-tailed test, you need to find the probability that the Z-statistic is at least as extreme as 2.35 in either direction (both positive and negative).

3. Use the standard normal distribution table: Look up the Z-statistic of 2.35 in the standard normal distribution table (or use a calculator or software that provides the cumulative distribution function for the standard normal distribution).

4. Find the cumulative probability: The cumulative probability for a Z-statistic of 2.35 is approximately 0.9906. This represents the probability that a value is less than 2.35.

5. Calculate the tail probability: Since the test is 2-tailed, you need to consider both tails. The probability in one tail is 1 - 0.9906 = 0.0094.

6. Double the tail probability: For a 2-tailed test, you double the tail probability to account for both tails. So, the P-value is 2 * 0.0094 = 0.0188.

7. Round to three decimal places: The P-value rounded to three decimal places is 0.019.

Therefore, the P-value is 0.019.