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.