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Proctored Nonproctored A study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. μ H₁ H₂ n 33 32 X 78.35 86.03 S 10.17 22.02

Proctored Nonproctored A study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. μ H₁ H₂ n 33 32 X 78.35 86.03 S 10.17 22.02

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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### Proctored vs. Nonproctored Test Scores Study A study was performed to compare the performance of students on proctored tests versus nonproctored tests. The results of the study are shown in the table below. The two samples are assumed to be independent, simple random samples selected from normally distributed populations, and it is assumed that the population standard deviations are equal. | | Proctored (\( \mu_1 \)) | Nonproctored (\( \mu_2 \)) | |---------------------|-------------------------|---------------------------| | Sample Size (n) | 33 | 32 | | Mean (x̄) | 78.35 | 86.03 | | Standard Deviation (s) | 10.17 | 22.02 | ### Hypothesis Testing **Objective:** Use a 0.05 significance level to test the claim that students taking nonproctored tests achieve higher mean scores than those taking proctored tests. #### What are the Null and Alternative Hypotheses? - Option A: - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 < \mu_2 \) - Option B: - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 \neq \mu_2 \) - Option C: - \( H_0: \mu_1 \neq \mu_2 \) - \( H_1: \mu_1 < \mu_2 \) - Option D: - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 > \mu_2 \) ### Calculations 1. **Test Statistic Calculation:** - The test statistic, \( t \), is \( \_\_\_\_ \) (Round to two decimal places as needed.) 2. **P-Value Calculation:** - The P-value is \( \_\_\_\_ \) (Round to three decimal places as needed.) ### Conclusion Depending on the calculations of the test statistic and P-value, the possible conclusions are: - Option A: - Reject \( H_0 \). There is not sufficient evidence to support
Transcribed Image Text:### Proctored vs. Nonproctored Test Scores Study A study was performed to compare the performance of students on proctored tests versus nonproctored tests. The results of the study are shown in the table below. The two samples are assumed to be independent, simple random samples selected from normally distributed populations, and it is assumed that the population standard deviations are equal. | | Proctored (\( \mu_1 \)) | Nonproctored (\( \mu_2 \)) | |---------------------|-------------------------|---------------------------| | Sample Size (n) | 33 | 32 | | Mean (x̄) | 78.35 | 86.03 | | Standard Deviation (s) | 10.17 | 22.02 | ### Hypothesis Testing **Objective:** Use a 0.05 significance level to test the claim that students taking nonproctored tests achieve higher mean scores than those taking proctored tests. #### What are the Null and Alternative Hypotheses? - Option A: - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 < \mu_2 \) - Option B: - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 \neq \mu_2 \) - Option C: - \( H_0: \mu_1 \neq \mu_2 \) - \( H_1: \mu_1 < \mu_2 \) - Option D: - \( H_0: \mu_1 = \mu_2 \) - \( H_1: \mu_1 > \mu_2 \) ### Calculations 1. **Test Statistic Calculation:** - The test statistic, \( t \), is \( \_\_\_\_ \) (Round to two decimal places as needed.) 2. **P-Value Calculation:** - The P-value is \( \_\_\_\_ \) (Round to three decimal places as needed.) ### Conclusion Depending on the calculations of the test statistic and P-value, the possible conclusions are: - Option A: - Reject \( H_0 \). There is not sufficient evidence to support
### Educational Resource: Analysis of Proctored vs. Nonproctored Tests #### Study Overview A study was conducted to compare scores from proctored and nonproctored tests. The results are summarized in the table below. Assume that the two samples are independent random samples selected from normally distributed populations. Additionally, the population standard deviations are not presumed to be equal. #### Data Summary The table below provides data on the samples for proctored and nonproctored tests: | | Proctored (\( H_1 \)) | Nonproctored (\( H_2 \)) | |--------------------------|-----------------------|--------------------------| | Sample Size (\( n \)) | 33 | 32 | | Mean (\( \bar{x} \)) | 78.35 | 86.03 | | Standard Deviation (\( s \)) | 10.17 | 22.02 | ### Statistical Analysis #### (a) Hypothesis Testing 1. **Calculate the Test Statistic:** \( t = \) \[ \_\_\_\_ \] (Round to three decimal places as needed.) 2. **P-value:** The P-value is \( \_\_\_\_\) (Round to three decimal places as needed.) 3. **Conclusion of the Test:** Based on the P-value, determine the appropriate conclusion from the options below: - ○ A. Reject \( H_0 \). There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. - ○ B. Fail to reject \( H_0 \). There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. - ○ C. Fail to reject \( H_0 \). There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. - ○ D. Reject \( H_0 \). There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. #### (b) Confidence Interval Construction Construct a confidence interval suitable for testing the claim that students taking nonproctored tests get a higher mean score than those taking
Transcribed Image Text:### Educational Resource: Analysis of Proctored vs. Nonproctored Tests #### Study Overview A study was conducted to compare scores from proctored and nonproctored tests. The results are summarized in the table below. Assume that the two samples are independent random samples selected from normally distributed populations. Additionally, the population standard deviations are not presumed to be equal. #### Data Summary The table below provides data on the samples for proctored and nonproctored tests: | | Proctored (\( H_1 \)) | Nonproctored (\( H_2 \)) | |--------------------------|-----------------------|--------------------------| | Sample Size (\( n \)) | 33 | 32 | | Mean (\( \bar{x} \)) | 78.35 | 86.03 | | Standard Deviation (\( s \)) | 10.17 | 22.02 | ### Statistical Analysis #### (a) Hypothesis Testing 1. **Calculate the Test Statistic:** \( t = \) \[ \_\_\_\_ \] (Round to three decimal places as needed.) 2. **P-value:** The P-value is \( \_\_\_\_\) (Round to three decimal places as needed.) 3. **Conclusion of the Test:** Based on the P-value, determine the appropriate conclusion from the options below: - ○ A. Reject \( H_0 \). There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. - ○ B. Fail to reject \( H_0 \). There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. - ○ C. Fail to reject \( H_0 \). There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. - ○ D. Reject \( H_0 \). There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. #### (b) Confidence Interval Construction Construct a confidence interval suitable for testing the claim that students taking nonproctored tests get a higher mean score than those taking
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