What is the p-value of a left-tailed one-mean hypothesis test, with a test statistic of z0=−0.97? (Do not round your answer; compute your answer using a value from the table below.)
z−1.2−1.1−1.0−0.90.000.1150.1360.1590.1840.010.1130.1330.1560.1810.020.1110.1310.1540.1790.030.1090.1290.1520.1760.040.1070.1270.1490.1740.050.1060.1250.1470.1710.060.1040.1230.1450.1690.070.1020.1210.1420.1660.080.1000.1190.1400.1640.090.0990.1170.1380.161
Provide your answer below:

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.

Learn how to calculate the p-value for a left-tailed one-mean hypothesis test with a given test statistic of z = -0.97. This problem involves using statistical tables and interpolation techniques to estimate the p-value accurately.

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