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Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence interval of (1.8,3.2) when estimating the mean height (in centimeters) of a sample of seedlings. ..... The estimated margin of error is.

Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence interval of (1.8,3.2) when estimating the mean height (in centimeters) of a sample of seedlings. ..... The estimated margin of error is.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Using Confidence Intervals to Estimate Margin of Error and Sample Mean** When working with data, confidence intervals provide a range within which we expect the true value of a parameter, such as the mean, to lie. The margin of error is an essential component, representing the extent to which the sample mean might differ from the true mean. **Example Scenario:** A biologist reports a confidence interval of (1.8, 3.2) when estimating the mean height (in centimeters) of a sample of seedlings. **Determining the Estimated Margin of Error:** The margin of error is calculated as half the width of the confidence interval. To find this: 1. Identify the endpoints of the confidence interval: - Lower limit (L) = 1.8 - Upper limit (U) = 3.2 2. Calculate the margin of error (ME) as: \[ ME = \frac{U - L}{2} = \frac{3.2 - 1.8}{2} = 0.7 \] **Calculating the Sample Mean:** The sample mean can be estimated as the midpoint of the confidence interval: - Sample Mean = \(\frac{L + U}{2} = \frac{1.8 + 3.2}{2} = 2.5\) Therefore, the estimated margin of error is **0.7** cm, and the estimated sample mean is **2.5** cm. **Interactive Tools:** For further practice, utilize the following features: - **Help Me Solve This**: Get step-by-step guidance for similar problems. - **View an Example**: Review solved examples to understand the process better. - **Get More Help**: Access additional resources for deeper learning. Feel free to use these tools to enhance your understanding of statistical concepts.
Transcribed Image Text:**Using Confidence Intervals to Estimate Margin of Error and Sample Mean** When working with data, confidence intervals provide a range within which we expect the true value of a parameter, such as the mean, to lie. The margin of error is an essential component, representing the extent to which the sample mean might differ from the true mean. **Example Scenario:** A biologist reports a confidence interval of (1.8, 3.2) when estimating the mean height (in centimeters) of a sample of seedlings. **Determining the Estimated Margin of Error:** The margin of error is calculated as half the width of the confidence interval. To find this: 1. Identify the endpoints of the confidence interval: - Lower limit (L) = 1.8 - Upper limit (U) = 3.2 2. Calculate the margin of error (ME) as: \[ ME = \frac{U - L}{2} = \frac{3.2 - 1.8}{2} = 0.7 \] **Calculating the Sample Mean:** The sample mean can be estimated as the midpoint of the confidence interval: - Sample Mean = \(\frac{L + U}{2} = \frac{1.8 + 3.2}{2} = 2.5\) Therefore, the estimated margin of error is **0.7** cm, and the estimated sample mean is **2.5** cm. **Interactive Tools:** For further practice, utilize the following features: - **Help Me Solve This**: Get step-by-step guidance for similar problems. - **View an Example**: Review solved examples to understand the process better. - **Get More Help**: Access additional resources for deeper learning. Feel free to use these tools to enhance your understanding of statistical concepts.
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