Use the given information to find the p-value: the test statistic is a two-tailed test and z=-2.75 (normal distribution).

Question

Round your answer to nearest thousandths.

Answer 1

To find the p-value for a two-tailed test with a test statistic \( z = -2.75 \), we can use the standard normal distribution.

1. Find the area (or probability) to the left of \( z = -2.75 \) using the standard normal distribution table (or a calculator).
2. Since the z-table typically provides values for the cumulative area from the left up to a given z-value, we find that the area to the left of \( z = -2.75 \) is approximately \( 0.0030 \).
3. For a two-tailed test, we need to multiply this area by 2 because we want the area in both tails of the distribution: \[ p\text{-value} = 2 \times P(Z < -2.75) \]
4. Therefore: \[ p\text{-value} = 2 \times 0.0030 = 0.0060 \]

So, the p-value is approximately \( 0.006 \) when rounded to the nearest thousandths.