Answer :
To find the p-value in a two-tail hypothesis test when given a Z-score (ZSTAT) of 1.57, you can follow these steps:
Understand the Concept:
- A p-value in hypothesis testing is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. In a two-tailed test, we are interested in deviations in both directions away from the null hypothesis.
Find the Probability Corresponding to ZSTAT:
- Use a standard normal distribution (Z) table or a calculator with statistical functions to find the probability that Z is less than 1.57. This tells you the area to the left of 1.57 on the normal distribution curve.
- Typically, the Z table gives the cumulative probability from the left up to the given Z-score.
Locate the Cumulative Probability:
- For Z = 1.57:
- Using a Z-table or calculator, we find that P(Z < 1.57) ≈ 0.9418. This means there is about a 94.18% probability of observing a value less than 1.57.
- For Z = 1.57:
Calculate the Two-Tailed P-value:
- In a two-tailed test, you must account for the extreme in both directions (negative and positive deviation from the mean). Therefore, you calculate:
- Probability of Z being greater than 1.57 is 1 - P(Z < 1.57) = 1 - 0.9418 = 0.0582.
- Since the test is two-tailed, you multiply this probability by 2: \( p = 2 \times 0.0582 = 0.1164 \).
- Therefore, the p-value is approximately 0.1164.
- In a two-tailed test, you must account for the extreme in both directions (negative and positive deviation from the mean). Therefore, you calculate:
Interpret the Result:
- If this p-value is greater than your significance level (commonly 0.05), you would fail to reject the null hypothesis. This suggests there isn't enough evidence to support a significant effect or difference.
It's important to ensure you are using an accurate Z-table and understand when to apply the two-tailed calculation correctly.
