Provided below are summary statistics for independent simple random samples from two populations. Use the pooled t-test and the pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. X = 22, 5, = 6, n1 = 22, x2 = 25, s, = 7, n = 14 a. Left-tailed test, a =0.05 b. 90% confidence interval a. What are the correct hypotheses for a left-tailed test? O B. Ho: 4 "2 O A. Ho: 41 > H2 Hi =2 OC. Ho: H1 <2 OD. Ho: 4 "2 OF. Ho: 4 "H2 H: 2 OE. Ho: H2 Compute the test statistic.
Provided below are summary statistics for independent simple random samples from two populations. Use the pooled t-test and the pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. X = 22, 5, = 6, n1 = 22, x2 = 25, s, = 7, n = 14 a. Left-tailed test, a =0.05 b. 90% confidence interval a. What are the correct hypotheses for a left-tailed test? O B. Ho: 4 "2 O A. Ho: 41 > H2 Hi =2 OC. Ho: H1 <2 OD. Ho: 4 "2 OF. Ho: 4 "H2 H: 2 OE. Ho: H2 Compute the test statistic.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 7PPS
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5c84145-a33d-498c-9246-5dc8646df0e1%2F0b81e8c3-bdd0-412f-8495-4c02903a0837%2F07hcush_processed.jpeg&w=3840&q=75)
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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