Question

What is the p-value of a **two-tailed** one-mean hypothesis test, with a test statistic of z0=−1.01? (Do not round your answer; compute your answer using a value from the table below.)z0.000.010.020.030.040.050.060.070.080.09−1.20.1150.1130.1110.1090.1070.1060.1040.1020.1000.099−1.10.1360.1330.1310.1290.1270.1250.1230.1210.1190.117−1.00.1590.1560.1540.1520.1490.1470.1450.1420.1400.138−0.90.1840.1810.1790.1760.1740.1710.1690.1660.1640.161

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To find the **p-value** for a **two-tailed** hypothesis test with a given \( z_0 = -1.01 \), we follow these steps:

### Step 1: Locate the closest z-value from the table
Looking at the table provided, we see that \( z_0 = -1.01 \) lies between \( z = -1.00 \) and \( z = -1.02 \). The closest values we can refer to are:

- \( z = -1.00 \), which corresponds to a value of **0.158**
- \( z = -1.02 \) (not listed, but we can interpolate between values)

Since \( z_0 = -1.01 \) is quite close to \( z = -1.00 \), we can approximate the area under the curve (the cumulative probability) using the value for \( z = -1.00 \), which is **0.158**.

### Step 2: Compute the p-value for the two-tailed test
For a **two-tailed test**, the p-value is twice the area in the tail beyond the absolute value of \( z_0 \). Since \( z_0 = -1.01 \), we use the area under the curve for \( z = 1.01 \).

The area in one tail is approximately **0.158** (from the table), so for a two-tailed test, the p-value is:

\[
p\text{-value} = 2 \times 0.158 = 0.316
\]

### Final Answer:
The p-value for the two-tailed test is approximately **0.316**.

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Would you like more details on how the p-value is used, or any other clarifications?

Here are 5 related questions:
1. What is the interpretation of a p-value in hypothesis testing?
2. How do you determine whether to reject the null hypothesis using the p-value?
3. What is the difference between one-tailed and two-tailed hypothesis tests?
4. How would the p-value change for a different z-score (e.g., \( z_0 = 1.96 \))?
5. What is the critical value for a two-tailed test at a 5% significance level?

**Tip:** When using p-values, always compare them to your significance level (α) to decide whether to reject the null hypothesis.

What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=−1.01?

Learn how to calculate the p-value for a two-tailed hypothesis test with z0 = -1.01. This step-by-step guide explains the use of z-scores, the standard normal distribution, and hypothesis testing. Suitable for college-level statistics students.

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