MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:**Hypothesis Testing with Significance Level 0.10**
**Step 3: Enter the Test Statistic**
- Calculation: Round to 3 decimal places.
- Test Statistic Value: 2.041
**Visual Demonstration**
The image includes two bell curves on either side of the test statistic:
1. **Left Bell Curve:**
- The area under the curve to the left of \( z_{\alpha/2} = -1.645 \) is shaded, indicating the rejection region on the negative side.
2. **Right Bell Curve:**
- The area under the curve to the right of \( z = 2.041 \) is shaded, marking the rejection region on the positive side.
- The critical value is \( z_{\alpha/2} = 1.645 \).
**Decision Making**
**(b) Analyzing the Test Statistic:**
- Determine if the test statistic falls within the rejection region.
- Options:
- The value of the test statistic lies in the rejection region.
- The value of the test statistic doesn't lie in the rejection region.
- Response Options: Checkboxes next to each statement allow selection.
**(c) Conclusion at 0.10 Level of Significance:**
- Decide on the null hypothesis based on previous analysis.
- Options:
- The null hypothesis should be rejected.
- The null hypothesis should not be rejected.
- Response Options: Checkboxes next to each statement allow selection.
**Interactive Elements**
- Buttons for "Explanation" and "Check" findings.
This layout and questioning guide students through the concepts of hypothesis testing, focusing on critical thinking and accurate decision-making based on statistical evidence in a two-tailed test.
![Suppose there is a claim that a certain population has a mean, μ, that is different than 9. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.10 level of significance. To start this test, you write the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) as follows:
\[ H_0: \mu = 9 \]
\[ H_1: \mu \neq 9 \]
Suppose you also know the following information:
The critical values are -1.645 and 1.645 (rounded to 3 decimal places).
The value of the test statistic is 2.041 (rounded to 3 decimal places).
(a) Complete the steps below to show the rejection region(s) and the value of the test statistic for this test.
**Standard Normal Distribution**
- **Step 1:** Select one-tailed or two-tailed.
- One-tailed
- Two-tailed (selected)
- **Step 2:** Enter the critical value(s). (Round to 3 decimal places.)
- -1.645, 1.645
- **Step 3:** Enter the test statistic. (Round to 3 decimal places.)
- 2.041
**Graph Explanation:**
The graph represents a standard normal distribution. It is a bell-shaped curve centered around a mean of 0. The x-axis represents the z-scores, while the y-axis represents the probability density. Critical values of -1.645 and 1.645 are marked on the x-axis, creating two rejection regions in the tails of the distribution. The test statistic of 2.041 is plotted on the x-axis, falling into the rejection region on the right side.](https://content.bartleby.com/qna-images/question/b5da94fe-19e7-4c6f-a636-47d7a1fa1ee8/37a2c306-624b-41ea-a89b-50b5924c0fc2/glefgc9f_processed.jpeg)
Transcribed Image Text:Suppose there is a claim that a certain population has a mean, μ, that is different than 9. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.10 level of significance. To start this test, you write the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) as follows:
\[ H_0: \mu = 9 \]
\[ H_1: \mu \neq 9 \]
Suppose you also know the following information:
The critical values are -1.645 and 1.645 (rounded to 3 decimal places).
The value of the test statistic is 2.041 (rounded to 3 decimal places).
(a) Complete the steps below to show the rejection region(s) and the value of the test statistic for this test.
**Standard Normal Distribution**
- **Step 1:** Select one-tailed or two-tailed.
- One-tailed
- Two-tailed (selected)
- **Step 2:** Enter the critical value(s). (Round to 3 decimal places.)
- -1.645, 1.645
- **Step 3:** Enter the test statistic. (Round to 3 decimal places.)
- 2.041
**Graph Explanation:**
The graph represents a standard normal distribution. It is a bell-shaped curve centered around a mean of 0. The x-axis represents the z-scores, while the y-axis represents the probability density. Critical values of -1.645 and 1.645 are marked on the x-axis, creating two rejection regions in the tails of the distribution. The test statistic of 2.041 is plotted on the x-axis, falling into the rejection region on the right side.
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