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4. Construct the 95% confidence interval for µ₁ − µ2, the average score difference between group A and B. Please show your derivation steps, no calculations is needed. (1). Derive the distribution of Y₁. - Y2. and construct the 95% confidence interval for ₁-₂ when the variance o² is known.

4. Construct the 95% confidence interval for µ₁ − µ2, the average score difference between group A and B. Please show your derivation steps, no calculations is needed. (1). Derive the distribution of Y₁. - Y2. and construct the 95% confidence interval for ₁-₂ when the variance o² is known.

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
Problem 1P
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**Question 4:** Construct the 95% confidence interval for \( \mu_1 - \mu_2 \), the average score difference between group A and B. Please show your derivation steps; no calculations are needed. 1. Derive the distribution of \( \overline{Y}_1 - \overline{Y}_2 \), and construct the 95% confidence interval for \( \mu_1 - \mu_2 \) when the variance \( \sigma^2 \) is known.
Transcribed Image Text:**Question 4:** Construct the 95% confidence interval for \( \mu_1 - \mu_2 \), the average score difference between group A and B. Please show your derivation steps; no calculations are needed. 1. Derive the distribution of \( \overline{Y}_1 - \overline{Y}_2 \), and construct the 95% confidence interval for \( \mu_1 - \mu_2 \) when the variance \( \sigma^2 \) is known.
**Setup:** In an experiment to compare different methods of teaching arithmetic, a group of students were randomly divided into three equal-sized groups. Group A was taught by the current method, while the other two groups were taught by one of two new methods. At the end, each student took a standardized test, with the following results: | Group | Score | \(\bar{Y}_{i\cdot}\) | \((\bar{Y}_{i\cdot} - \bar{Y}_{\cdot\cdot})^2\) | \(s_i^2\) | |-------|---------------------|----------------------|-----------------------------------|----------| | A | 17 14 24 20 24 23 16 15 14 | 18.55 | 0.664 | 18.03 | | B | 19 28 26 26 19 24 24 23 22 | 23.44 | 16.60 | 9.53 | | C | 21 14 13 19 15 10 10 18 20 | 16.11 | 10.62 | 13.11 | | Grand | | 19.37 | | | ### Table Explanation: - **Group:** Represents the group label; A, B, and C. - **Score:** Lists the scores obtained by students in each group on the standardized test. - \(\bar{Y}_{i\cdot}\): Represents the mean score for each group. - \((\bar{Y}_{i\cdot} - \bar{Y}_{\cdot\cdot})^2\): Denotes the squared difference between the group's mean score and the overall mean score across all groups. - \(s_i^2\): Represents the variance of students' scores within each group.
Transcribed Image Text:**Setup:** In an experiment to compare different methods of teaching arithmetic, a group of students were randomly divided into three equal-sized groups. Group A was taught by the current method, while the other two groups were taught by one of two new methods. At the end, each student took a standardized test, with the following results: | Group | Score | \(\bar{Y}_{i\cdot}\) | \((\bar{Y}_{i\cdot} - \bar{Y}_{\cdot\cdot})^2\) | \(s_i^2\) | |-------|---------------------|----------------------|-----------------------------------|----------| | A | 17 14 24 20 24 23 16 15 14 | 18.55 | 0.664 | 18.03 | | B | 19 28 26 26 19 24 24 23 22 | 23.44 | 16.60 | 9.53 | | C | 21 14 13 19 15 10 10 18 20 | 16.11 | 10.62 | 13.11 | | Grand | | 19.37 | | | ### Table Explanation: - **Group:** Represents the group label; A, B, and C. - **Score:** Lists the scores obtained by students in each group on the standardized test. - \(\bar{Y}_{i\cdot}\): Represents the mean score for each group. - \((\bar{Y}_{i\cdot} - \bar{Y}_{\cdot\cdot})^2\): Denotes the squared difference between the group's mean score and the overall mean score across all groups. - \(s_i^2\): Represents the variance of students' scores within each group.
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