Find the P-value for a left-tailed hypothesis test with a test statistic of z= - 1.77. Decide whether to reject H, if the level of significance is a = 0.10. P-value = (Round to four decimal places as needed.)

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**Hypothesis Testing: Left-Tailed Test**

Find the P-value for a left-tailed hypothesis test with a test statistic of \( z = -1.77 \). Decide whether to reject \( H_0 \) if the level of significance is \( \alpha = 0.10 \).

**P-value:** \[ \boxed{\phantom{0}} \] (Round to four decimal places as needed.) 

**Explanation:**

In this scenario, we're conducting a left-tailed test, which means we are testing whether a sample mean is significantly less than the hypothesized population mean. The z-score for this test is -1.77. To determine the P-value, we will look up this z-score in the standard normal distribution table.

*Steps to Determine the P-value:*

1. **Identify the Z-score:**
   - The provided test statistic is \( z = -1.77 \).

2. **Find the P-value:**
   - Using a Z-table or statistical software, locate the probability corresponding to \( z = -1.77 \).

3. **Comparison with the Level of Significance:**
   - Compare the P-value to the given level of significance (\( \alpha = 0.10 \)).
   - If the P-value is less than or equal to \( \alpha \), reject the null hypothesis \( H_0 \).
   - If the P-value is greater than \( \alpha \), do not reject \( H_0 \).

This process helps to determine whether the observed data is significantly different from what was expected under the null hypothesis.
Transcribed Image Text:**Hypothesis Testing: Left-Tailed Test** Find the P-value for a left-tailed hypothesis test with a test statistic of \( z = -1.77 \). Decide whether to reject \( H_0 \) if the level of significance is \( \alpha = 0.10 \). **P-value:** \[ \boxed{\phantom{0}} \] (Round to four decimal places as needed.) **Explanation:** In this scenario, we're conducting a left-tailed test, which means we are testing whether a sample mean is significantly less than the hypothesized population mean. The z-score for this test is -1.77. To determine the P-value, we will look up this z-score in the standard normal distribution table. *Steps to Determine the P-value:* 1. **Identify the Z-score:** - The provided test statistic is \( z = -1.77 \). 2. **Find the P-value:** - Using a Z-table or statistical software, locate the probability corresponding to \( z = -1.77 \). 3. **Comparison with the Level of Significance:** - Compare the P-value to the given level of significance (\( \alpha = 0.10 \)). - If the P-value is less than or equal to \( \alpha \), reject the null hypothesis \( H_0 \). - If the P-value is greater than \( \alpha \), do not reject \( H_0 \). This process helps to determine whether the observed data is significantly different from what was expected under the null hypothesis.
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