Use a t-distribution to find a confidence interval for the difference in means μ = ₁-₂ using the relevant sample results from paired data. Assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using d = x₁ - x₂. A 95% confidence interval for using the paired difference sample results x = 1.4, sa = 2.0, na = 30. Give the best estimate for u, the margin of error, and the confidence interval. Enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places. Best estimate- Margin of error- The 95% confidence interval is i Save for Later to
Use a t-distribution to find a confidence interval for the difference in means μ = ₁-₂ using the relevant sample results from paired data. Assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using d = x₁ - x₂. A 95% confidence interval for using the paired difference sample results x = 1.4, sa = 2.0, na = 30. Give the best estimate for u, the margin of error, and the confidence interval. Enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places. Best estimate- Margin of error- The 95% confidence interval is i Save for Later to
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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![**Title: Calculating a Confidence Interval for Paired Sample Data**
**Introduction**
In statistics, a t-distribution is often used to find a confidence interval for the difference in means between two paired samples. This is particularly useful when the results come from random samples from two populations that are approximately normally distributed. This guide explains how to compute the confidence interval for paired sample data by using a specific example.
**Example Problem**
We want to find a 95% confidence interval for the difference in means \( \mu_d = \mu_1 - \mu_2 \).
**Given Data**
- Mean of differences \( \bar{x}_d = 1.4 \)
- Standard deviation of differences \( s_d = 2.0 \)
- Sample size \( n_d = 30 \)
**Instructions**
1. **Best Estimate for \( \mu_d \):**
- The best estimate is the sample mean difference, \( \bar{x}_d \).
2. **Calculate Margin of Error:**
- Use the formula for margin of error in the context of a t-distribution with the given standard deviation and sample size.
3. **Compute the Confidence Interval:**
- The interval should be calculated using the best estimate plus or minus the margin of error to find the lower and upper bounds of the confidence interval.
**Response Fields**
- **Best estimate =** [Input Box]
- **Margin of error =** [Input Box]
- **The 95% confidence interval is** [Input Box] to [Input Box]
**Conclusion**
By following these instructions, you can accurately determine the confidence interval for the difference in means in a paired sample scenario, which helps in understanding the range within which the true difference in population means likely falls.
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Transcribed Image Text:**Title: Calculating a Confidence Interval for Paired Sample Data**
**Introduction**
In statistics, a t-distribution is often used to find a confidence interval for the difference in means between two paired samples. This is particularly useful when the results come from random samples from two populations that are approximately normally distributed. This guide explains how to compute the confidence interval for paired sample data by using a specific example.
**Example Problem**
We want to find a 95% confidence interval for the difference in means \( \mu_d = \mu_1 - \mu_2 \).
**Given Data**
- Mean of differences \( \bar{x}_d = 1.4 \)
- Standard deviation of differences \( s_d = 2.0 \)
- Sample size \( n_d = 30 \)
**Instructions**
1. **Best Estimate for \( \mu_d \):**
- The best estimate is the sample mean difference, \( \bar{x}_d \).
2. **Calculate Margin of Error:**
- Use the formula for margin of error in the context of a t-distribution with the given standard deviation and sample size.
3. **Compute the Confidence Interval:**
- The interval should be calculated using the best estimate plus or minus the margin of error to find the lower and upper bounds of the confidence interval.
**Response Fields**
- **Best estimate =** [Input Box]
- **Margin of error =** [Input Box]
- **The 95% confidence interval is** [Input Box] to [Input Box]
**Conclusion**
By following these instructions, you can accurately determine the confidence interval for the difference in means in a paired sample scenario, which helps in understanding the range within which the true difference in population means likely falls.
[Save for Later Button]
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