Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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![### Statistical Analysis of Independent Samples
**Given Summary Statistics:**
- Sample 1: \( \bar{x}_1 = 22 \), \( s_1 = 6 \), \( n_1 = 22 \)
- Sample 2: \( \bar{x}_2 = 25 \), \( s_2 = 7 \), \( n_2 = 14 \)
**Analysis Requirements:**
- **Test Type:** Left-tailed test, \( \alpha = 0.05 \)
- **Confidence Interval:** 90% confidence interval
### Step-by-Step Procedure:
#### a. Determine the Correct Hypotheses for a Left-Tailed Test
From the provided options, select the correct hypotheses:
- **Option A:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_a: \mu_1 \neq \mu_2 \)
- **Option B:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_a: \mu_1 > \mu_2 \)
- **Option C:**
- \( H_0: \mu_1 \geq \mu_2 \)
- \( H_a: \mu_1 < \mu_2 \)
- **Option D:**
- \( H_0: \mu_1 \leq \mu_2 \)
- \( H_a: \mu_1 > \mu_2 \)
- **Option E:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_a: \mu_1 \leq \mu_2 \)
- **Option F:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_a: \mu_1 \neq \mu_2 \)
#### b. Compute the Test Statistic
- Compute the test statistic \( t = \) (Round to three decimal places as needed).
#### c. Determine the Critical Value
- Determine the critical value \( -t_{\alpha} = \) (Round to three decimal places as needed).
#### d. Conclusion of the Hypothesis Test
- Conclude based on the test statistic and critical value:
- Since the test statistic \( t \) [selection box with options] the](https://content.bartleby.com/qna-images/question/d5c84145-a33d-498c-9246-5dc8646df0e1/0b81e8c3-bdd0-412f-8495-4c02903a0837/07hcush_processed.jpeg)
Transcribed Image Text:### Statistical Analysis of Independent Samples
**Given Summary Statistics:**
- Sample 1: \( \bar{x}_1 = 22 \), \( s_1 = 6 \), \( n_1 = 22 \)
- Sample 2: \( \bar{x}_2 = 25 \), \( s_2 = 7 \), \( n_2 = 14 \)
**Analysis Requirements:**
- **Test Type:** Left-tailed test, \( \alpha = 0.05 \)
- **Confidence Interval:** 90% confidence interval
### Step-by-Step Procedure:
#### a. Determine the Correct Hypotheses for a Left-Tailed Test
From the provided options, select the correct hypotheses:
- **Option A:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_a: \mu_1 \neq \mu_2 \)
- **Option B:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_a: \mu_1 > \mu_2 \)
- **Option C:**
- \( H_0: \mu_1 \geq \mu_2 \)
- \( H_a: \mu_1 < \mu_2 \)
- **Option D:**
- \( H_0: \mu_1 \leq \mu_2 \)
- \( H_a: \mu_1 > \mu_2 \)
- **Option E:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_a: \mu_1 \leq \mu_2 \)
- **Option F:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_a: \mu_1 \neq \mu_2 \)
#### b. Compute the Test Statistic
- Compute the test statistic \( t = \) (Round to three decimal places as needed).
#### c. Determine the Critical Value
- Determine the critical value \( -t_{\alpha} = \) (Round to three decimal places as needed).
#### d. Conclusion of the Hypothesis Test
- Conclude based on the test statistic and critical value:
- Since the test statistic \( t \) [selection box with options] the
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