A common final examination was administered to each student enrolled in Sociology 1 Introduction t Sociology. Students enrolled in daytime, evening, and online sections of this course were randomly selected, and their final examination scores were recorded. The sample data are compiled below. Section Final Examination Scores of Students in Sociology 1 Introduction to Sociology Daytime 86 77 64 88 81 75 90 78 59 66 Evening 76 53 86 65 85 84 74 61 89 70 Online 78 86 54 60 47 70 62 78 93 65 Conduct a hypothesis test, at the 5% level of significance, to determine whether the mean final examination score of Sociology 1 students enrolled in daytime, evening, and online sections are all equal.

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### Educational Content on Sociology 1 Examination Results

A common final examination was administered to each student enrolled in Sociology 1: Introduction to Sociology. Students enrolled in the daytime, evening, and online sections of this course were randomly selected, and their final examination scores were recorded. The sample data are compiled below:

#### Final Examination Scores of Students in Sociology 1

- **Daytime Section:**
  - Scores: 86, 77, 64, 88, 81, 75, 78, 59, 66

- **Evening Section:**
  - Scores: 76, 53, 86, 65, 85, 84, 74, 61, 89, 70

- **Online Section:**
  - Scores: 78, 86, 54, 60, 47, 70, 62, 78, 93, 65

#### Analysis Task

Conduct a hypothesis test, at the 5% level of significance, to determine whether the mean final examination score of Sociology 1 students enrolled in daytime, evening, and online sections are all equal.

In this analysis, you will:

1. **Identify the Null and Alternative Hypotheses:**
   - Null Hypothesis (\(H_0\)): The mean scores of the three sections (daytime, evening, online) are equal.
   - Alternative Hypothesis (\(H_a\)): At least one section’s mean score is different.

2. **Select an Appropriate Statistical Test:**
   - An ANOVA test is typically used for comparing the means of three or more groups.

3. **Determine Significance:**
   - Use a significance level (\(\alpha\)) of 0.05 to evaluate the results.

4. **Interpreting Results:**
   - After conducting the test, determine if \(H_0\) can be rejected or not based on the p-value obtained.

This exercise integrates statistical techniques into real-world academic assessment scenarios, enhancing data interpretation and evaluation skills.
Transcribed Image Text:### Educational Content on Sociology 1 Examination Results A common final examination was administered to each student enrolled in Sociology 1: Introduction to Sociology. Students enrolled in the daytime, evening, and online sections of this course were randomly selected, and their final examination scores were recorded. The sample data are compiled below: #### Final Examination Scores of Students in Sociology 1 - **Daytime Section:** - Scores: 86, 77, 64, 88, 81, 75, 78, 59, 66 - **Evening Section:** - Scores: 76, 53, 86, 65, 85, 84, 74, 61, 89, 70 - **Online Section:** - Scores: 78, 86, 54, 60, 47, 70, 62, 78, 93, 65 #### Analysis Task Conduct a hypothesis test, at the 5% level of significance, to determine whether the mean final examination score of Sociology 1 students enrolled in daytime, evening, and online sections are all equal. In this analysis, you will: 1. **Identify the Null and Alternative Hypotheses:** - Null Hypothesis (\(H_0\)): The mean scores of the three sections (daytime, evening, online) are equal. - Alternative Hypothesis (\(H_a\)): At least one section’s mean score is different. 2. **Select an Appropriate Statistical Test:** - An ANOVA test is typically used for comparing the means of three or more groups. 3. **Determine Significance:** - Use a significance level (\(\alpha\)) of 0.05 to evaluate the results. 4. **Interpreting Results:** - After conducting the test, determine if \(H_0\) can be rejected or not based on the p-value obtained. This exercise integrates statistical techniques into real-world academic assessment scenarios, enhancing data interpretation and evaluation skills.
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