To find the p-value for a left-tailed one-mean hypothesis test given the test statistic $z_0 = -0.97$, we can refer to the provided table.

We see that $z_0 = -0.97$ lies between $z = -1.0$ and $z = -0.9$.

Now, let's estimate the p-value by interpolating between the values given for $z = -1.0$ and $z = -0.9$:

• For $z = -1.0$, the p-value is 0.159.
• For $z = -0.9$, the p-value is 0.184.

Since $z_0 = -0.97$ is closer to $z = -1.0$ than to $z = -0.9$, the p-value will be closer to 0.159 than to 0.184.

To estimate, we can use linear interpolation:

$\text{Estimated p-value} = 0.159 + \frac{0.97 - 1.0}{-0.9 - (-1.0)} \times (0.184 - 0.159)$

Simplifying this:

$\text{Estimated p-value} = 0.159 + \frac{-0.03}{0.1} \times 0.025 = 0.159 + (-0.03 \times 0.25) = 0.159 - 0.0075 = 0.1515$

Thus, the estimated p-value is approximately 0.1515.

Would you like more details on how this estimation was done, or do you have any other questions?

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Related Questions:

1. What is the p-value for a right-tailed test with the same $z_0 = -0.97$?
2. How would the p-value change if the test statistic were $z_0 = -1.05$?
3. What does the p-value signify in the context of hypothesis testing?
4. How is the critical value determined for a left-tailed test at a given significance level?
5. What are the steps to perform a two-tailed hypothesis test using a z-statistic?

Tip: When interpolating values, the closer the statistic is to one of the reference points, the more accurate the interpolation.