## Comparison of Final Examination Scores: Today vs. Five Years AgoA statistics teacher aims to determine if there's a significant difference in the abilities of students enrolled in statistics today compared to those enrolled five years ago. The analysis uses a sample of final examination scores from students currently enrolled and those from five years prior. The data provided is as follows:### Data Summary:| | **Today** | **Five Years Ago** ||------------------|-----------|-------------------|| **Mean ($ \bar{x} $)** | 82 | 88 || **Variance ($ \sigma^2 $)** | 112.5 | 54 || **Sample Size ($ n $)** | 45 | 36 |### Explanation:1. **Mean ($ \bar{x} $)**: The average exam score for students today is 82, while it was 88 five years ago.2. **Variance ($ \sigma^2 $)**: The variance in exam scores is higher for today's students (112.5) compared to those from five years ago (54), indicating more variability in the current scores.3. **Sample Size ($ n $)**: The number of students sampled today is 45, whereas it was 36 five years ago.This information will help in conducting statistical tests to determine if the differences observed are statistically significant. The analysis may include hypothesis testing, confidence intervals, and other inference methods. ### Statistical Analysis Exercise Instructions**4. Refer to Exhibit 1.** The point estimate for the difference between the means of the two populations is:- A. 58.5- B. 9- C. -9- D. -6**5. Refer to Exhibit 1.** The standard error of $ \bar{X}_1 - \bar{X}_2 $ is:- A. 12.9- B. 9.3- C. 4- D. 2**6. Refer to Exhibit 1.** The 95% confidence interval for the difference between the two population means is:- A. -9.92 to -2.08- B. -3.92 to 3.92- C. -13.84 to 1.84- D. -24.228 to 12.23

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Description: ## Comparison of Final Examination Scores: Today vs. Five Years AgoA statistics teacher aims to determine if there's a significant difference in the abilities of students enrolled in statistics today compared to those enrolled five years ago. The an

Introduction: The 100 (1 – α) % confidence interval for the difference between population means, μ1…

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4. Refer to Exhibit 1. The point estimate for the difference between the means of the two populations is А. 58.5 B. 6. C. -9 D. -6 9. Refer to Exhibit 1. The standard error of x, -x, is A. 12.9 B. 9.3 С. D. 6. Refer to Exhibit 1. The 95º% confidence interval for the difference between the two population means is A. -9.92 to -2.08 B. -3.92 to 3.92 -13.84 to 1.84 -24.228 to 12.23 C. D. DFocus

4. Refer to Exhibit 1. The point estimate for the difference between the means of the two populations is А. 58.5 B. 6. C. -9 D. -6 9. Refer to Exhibit 1. The standard error of x, -x, is A. 12.9 B. 9.3 С. D. 6. Refer to Exhibit 1. The 95º% confidence interval for the difference between the two population means is A. -9.92 to -2.08 B. -3.92 to 3.92 -13.84 to 1.84 -24.228 to 12.23 C. D. DFocus

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## Comparison of Final Examination Scores: Today vs. Five Years Ago

A statistics teacher aims to determine if there's a significant difference in the abilities of students enrolled in statistics today compared to those enrolled five years ago. The analysis uses a sample of final examination scores from students currently enrolled and those from five years prior. The data provided is as follows:

### Data Summary:

| | **Today** | **Five Years Ago** |
|------------------|-----------|-------------------|
| **Mean ($ \bar{x} $)** | 82 | 88 |
| **Variance ($ \sigma^2 $)** | 112.5 | 54 |
| **Sample Size ($ n $)** | 45 | 36 |

### Explanation:

1. **Mean ($ \bar{x} $)**: The average exam score for students today is 82, while it was 88 five years ago.
2. **Variance ($ \sigma^2 $)**: The variance in exam scores is higher for today's students (112.5) compared to those from five years ago (54), indicating more variability in the current scores.
3. **Sample Size ($ n $)**: The number of students sampled today is 45, whereas it was 36 five years ago.

This information will help in conducting statistical tests to determine if the differences observed are statistically significant. The analysis may include hypothesis testing, confidence intervals, and other inference methods.

### Statistical Analysis Exercise Instructions

**4. Refer to Exhibit 1.** The point estimate for the difference between the means of the two populations is:
- A. 58.5
- B. 9
- C. -9
- D. -6

**5. Refer to Exhibit 1.** The standard error of $ \bar{X}_1 - \bar{X}_2 $ is:
- A. 12.9
- B. 9.3
- C. 4
- D. 2

**6. Refer to Exhibit 1.** The 95% confidence interval for the difference between the two population means is:
- A. -9.92 to -2.08
- B. -3.92 to 3.92
- C. -13.84 to 1.84
- D. -24.228 to 12.23

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