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3. Scarlett and Heather own an upscale restaurant in Dayton, Ohio, and want to study the spending habits of their customers. The results from a sample of 20 customers are as follows: Amount spent: xbar = $38.54, sample standard deviation = $7.26 Construct a 95% confidence interval estimate for the population mean amount spent per customer in the restaurant. Point Estimate Alpha Critical Value Standard Error Answers Margin of Error Confidence Interval Limits

3. Scarlett and Heather own an upscale restaurant in Dayton, Ohio, and want to study the spending habits of their customers. The results from a sample of 20 customers are as follows: Amount spent: xbar = $38.54, sample standard deviation = $7.26 Construct a 95% confidence interval estimate for the population mean amount spent per customer in the restaurant. Point Estimate Alpha Critical Value Standard Error Answers Margin of Error Confidence Interval Limits

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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### Confidence Interval Estimation for Average Spending **Problem Context:** Scarlett and Heather own an upscale restaurant in Dayton, Ohio, and want to study the spending habits of their customers. The results from a sample of 20 customers are as follows: - **Sample Mean (\(\bar{x}\))**: $38.54 - **Sample Standard Deviation**: $7.26 The task is to construct a 95% confidence interval estimate for the population mean amount spent per customer in the restaurant. **Diagram Explanation:** 1. **Bell Curve:** - The image features a bell-shaped curve which typically represents a normal distribution. This is used to visualize how data (such as spending amounts) is distributed around the mean value. 2. **Table of Answers:** - This is a table with columns labeled "Answers," providing structured spaces to fill out key statistical elements: - **Point Estimate**: The sample mean, representing the central value of the estimate. - **Alpha (α)**: Represents the significance level. In a 95% confidence interval, \( \alpha = 0.05 \). - **Critical Value**: Typically derived from a standard normal or t-distribution table depending on the sample size and variance knowledge. - **Standard Error**: Calculated using the sample standard deviation divided by the square root of the sample size. - **Margin of Error**: Derived from multiplying the critical value and the standard error. - **Confidence Interval Limits**: The range within which the true population mean is expected to lie, calculated as the sample mean ± the margin of error. These components together help in determining the confidence interval, providing an estimated range for the average amount customers spend at the restaurant.
Transcribed Image Text:### Confidence Interval Estimation for Average Spending **Problem Context:** Scarlett and Heather own an upscale restaurant in Dayton, Ohio, and want to study the spending habits of their customers. The results from a sample of 20 customers are as follows: - **Sample Mean (\(\bar{x}\))**: $38.54 - **Sample Standard Deviation**: $7.26 The task is to construct a 95% confidence interval estimate for the population mean amount spent per customer in the restaurant. **Diagram Explanation:** 1. **Bell Curve:** - The image features a bell-shaped curve which typically represents a normal distribution. This is used to visualize how data (such as spending amounts) is distributed around the mean value. 2. **Table of Answers:** - This is a table with columns labeled "Answers," providing structured spaces to fill out key statistical elements: - **Point Estimate**: The sample mean, representing the central value of the estimate. - **Alpha (α)**: Represents the significance level. In a 95% confidence interval, \( \alpha = 0.05 \). - **Critical Value**: Typically derived from a standard normal or t-distribution table depending on the sample size and variance knowledge. - **Standard Error**: Calculated using the sample standard deviation divided by the square root of the sample size. - **Margin of Error**: Derived from multiplying the critical value and the standard error. - **Confidence Interval Limits**: The range within which the true population mean is expected to lie, calculated as the sample mean ± the margin of error. These components together help in determining the confidence interval, providing an estimated range for the average amount customers spend at the restaurant.
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