MATLAB: An Introduction with Applications
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![**Finding the Margin of Error and Sample Mean from a Confidence Interval**
A store manager reports a confidence interval of (46.6, 79.2) when estimating the mean price (in dollars) for the population of textbooks.
To compute the estimated margin of error, use the following formula:
\[
\text{Margin of Error} = \frac{\text{Upper Limit} - \text{Lower Limit}}{2}
\]
Plug in the given values:
- Upper Limit = 79.2
- Lower Limit = 46.6
Calculate the margin of error and provide the result as an integer or a decimal.
After finding the margin of error, you can determine the sample mean using:
\[
\text{Sample Mean} = \frac{\text{Upper Limit} + \text{Lower Limit}}{2}
\]](https://content.bartleby.com/qna-images/question/993de58a-2778-4b88-a613-cf3a42e4d67b/c3619d88-5fbc-44cf-8e64-ce89d3ba4c56/6yu4ja9_processed.png)
Transcribed Image Text:**Finding the Margin of Error and Sample Mean from a Confidence Interval**
A store manager reports a confidence interval of (46.6, 79.2) when estimating the mean price (in dollars) for the population of textbooks.
To compute the estimated margin of error, use the following formula:
\[
\text{Margin of Error} = \frac{\text{Upper Limit} - \text{Lower Limit}}{2}
\]
Plug in the given values:
- Upper Limit = 79.2
- Lower Limit = 46.6
Calculate the margin of error and provide the result as an integer or a decimal.
After finding the margin of error, you can determine the sample mean using:
\[
\text{Sample Mean} = \frac{\text{Upper Limit} + \text{Lower Limit}}{2}
\]
![**Constructing a Confidence Interval for the Population Mean (μ)**
Given:
- Confidence level (c) = 0.98
- Sample mean (\( \bar{x} \)) = 15.3
- Population standard deviation (σ) = 5.0
- Sample size (n) = 55
To find a 98% confidence interval for \( μ \), the formula used is:
\[ \text{Confidence interval} = \left( \bar{x} - E, \bar{x} + E \right) \]
Where \( E \) is the margin of error calculated by:
\[ E = z \times \frac{σ}{\sqrt{n}} \]
Here, \( z \) is the z-score corresponding to the 98% confidence level. You can look up this value in a z-table or use a calculator.
The confidence interval for \( μ \) is displayed as \( (\ [ \ ), \( \ ], [ \ ), \( \ ] ) \).
*(Round to one decimal place as needed.)*
By substituting the values and calculating, you can determine the confidence interval.](https://content.bartleby.com/qna-images/question/993de58a-2778-4b88-a613-cf3a42e4d67b/c3619d88-5fbc-44cf-8e64-ce89d3ba4c56/7ohyukm_processed.png)
Transcribed Image Text:**Constructing a Confidence Interval for the Population Mean (μ)**
Given:
- Confidence level (c) = 0.98
- Sample mean (\( \bar{x} \)) = 15.3
- Population standard deviation (σ) = 5.0
- Sample size (n) = 55
To find a 98% confidence interval for \( μ \), the formula used is:
\[ \text{Confidence interval} = \left( \bar{x} - E, \bar{x} + E \right) \]
Where \( E \) is the margin of error calculated by:
\[ E = z \times \frac{σ}{\sqrt{n}} \]
Here, \( z \) is the z-score corresponding to the 98% confidence level. You can look up this value in a z-table or use a calculator.
The confidence interval for \( μ \) is displayed as \( (\ [ \ ), \( \ ], [ \ ), \( \ ] ) \).
*(Round to one decimal place as needed.)*
By substituting the values and calculating, you can determine the confidence interval.
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