ind the P-value for the indicated hypothesis test with the given standardized test statistic, z. Decide whether to reject Ho for the given level of significance a. Two-tailed test with test statistic z= -2.04 and α = 0.06 C "-value= (Round to four decimal places as needed.)

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## Hypothesis Testing: Finding the P-Value

To determine the P-value for a given hypothesis test with the provided standardized test statistic \( z \), follow these steps and decide whether to reject the null hypothesis (\( H_0 \)) for the specified level of significance \( \alpha \).

### Given:
- **Type of test:** Two-tailed
- **Test statistic:** \( z = -2.04 \)
- **Level of significance:** \( \alpha = 0.06 \)

### Step-by-step Solution:
1. **Find the P-value for the test statistic**: Using the standard normal distribution table or a calculator, lookup the P-value corresponding to \( z = -2.04 \).
   - P-value calculation includes finding the area under the curve to the left of \( z = -2.04 \) and then doubling it because it is a two-tailed test.

2. **Decision rule for rejecting \( H_0 \)**:
   - If the P-value is less than or equal to \( \alpha \), reject \( H_0 \).
   - If the P-value is greater than \( \alpha \), do not reject \( H_0 \).

### Answer:
```plaintext
P-value =  [  ]  (Round to four decimal places as needed.)
```

This section assists learners in understanding how to calculate and interpret the P-value in the context of hypothesis testing.
Transcribed Image Text:## Hypothesis Testing: Finding the P-Value To determine the P-value for a given hypothesis test with the provided standardized test statistic \( z \), follow these steps and decide whether to reject the null hypothesis (\( H_0 \)) for the specified level of significance \( \alpha \). ### Given: - **Type of test:** Two-tailed - **Test statistic:** \( z = -2.04 \) - **Level of significance:** \( \alpha = 0.06 \) ### Step-by-step Solution: 1. **Find the P-value for the test statistic**: Using the standard normal distribution table or a calculator, lookup the P-value corresponding to \( z = -2.04 \). - P-value calculation includes finding the area under the curve to the left of \( z = -2.04 \) and then doubling it because it is a two-tailed test. 2. **Decision rule for rejecting \( H_0 \)**: - If the P-value is less than or equal to \( \alpha \), reject \( H_0 \). - If the P-value is greater than \( \alpha \), do not reject \( H_0 \). ### Answer: ```plaintext P-value = [ ] (Round to four decimal places as needed.) ``` This section assists learners in understanding how to calculate and interpret the P-value in the context of hypothesis testing.
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