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.)
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.)
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F862166d3-ebd8-40df-9939-ca66a7942ca2%2F58dc224a-a797-4873-ac78-5c7c42043732%2F4bn3aga_processed.jpeg&w=3840&q=75)
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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