In a study of the accuracy of fast food drive-through orders, Restaurant A had 210 accurate orders and 63 that were not accurate. a. Construct a 95% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 95% confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.202
In a study of the accuracy of fast food drive-through orders, Restaurant A had 210 accurate orders and 63 that were not accurate. a. Construct a 95% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 95% confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.202
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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![**Educational Website Content: Understanding Confidence Intervals in Fast Food Order Accuracy**
### Study Overview
In a study investigating the accuracy of fast food drive-through orders, Restaurant A processed 210 orders accurately and had 63 orders that were not accurate. The study aims to:
1. Construct a 95% confidence interval estimate for the percentage of orders at Restaurant A that are not accurate.
2. Compare the interval from part (a) to a given 95% confidence interval for the percentage of inaccurate orders at Restaurant B, which ranges from 0.202 to 0.303.
### Part (a): Constructing the Confidence Interval
To construct the 95% confidence interval for Restaurant A’s percentage of inaccurate orders, we convert the percentage to a decimal format. We use the formula for constructing confidence intervals for proportions. *Note:* The actual computations are not shown here but reference standard statistical methods.
\[ \hat{p} = \frac{x}{n} \]
\[ \text{where: } \hat{p} = \text{proportion of inaccurate orders}, \]
\[ x = \text{number of inaccurate orders}, \]
\[ n = \text{total number of orders}. \]
### Part (b): Analyzing and Comparing the Intervals
**Choose the correct answer from the given options:**
- **A.** Since the upper confidence limit of the interval for Restaurant B is higher than both the lower and upper confidence limits of the interval for Restaurant A, this indicates that Restaurant B has a significantly higher percentage of inaccurate orders than Restaurant A.
- **B.** The lower confidence limit of the interval for Restaurant B is higher than the lower confidence limit of the interval for Restaurant A and the upper confidence limit of the interval for Restaurant B is also higher than the upper confidence limit of the interval for Restaurant A. Therefore, Restaurant B has a significantly higher percentage of inaccurate orders than Restaurant A.
- **C.** Since the two confidence intervals overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.
- **D.** No conclusion can be made because not enough information is given about the confidence interval for Restaurant B.
### Answer Analysis
Based on the given intervals:
- The confidence interval for Restaurant B is provided as 0.202 to 0.303.
- By comparing this interval to the one calculated for Restaurant A, conclusions can be drawn regarding the accuracy of the orders.
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Transcribed Image Text:**Educational Website Content: Understanding Confidence Intervals in Fast Food Order Accuracy**
### Study Overview
In a study investigating the accuracy of fast food drive-through orders, Restaurant A processed 210 orders accurately and had 63 orders that were not accurate. The study aims to:
1. Construct a 95% confidence interval estimate for the percentage of orders at Restaurant A that are not accurate.
2. Compare the interval from part (a) to a given 95% confidence interval for the percentage of inaccurate orders at Restaurant B, which ranges from 0.202 to 0.303.
### Part (a): Constructing the Confidence Interval
To construct the 95% confidence interval for Restaurant A’s percentage of inaccurate orders, we convert the percentage to a decimal format. We use the formula for constructing confidence intervals for proportions. *Note:* The actual computations are not shown here but reference standard statistical methods.
\[ \hat{p} = \frac{x}{n} \]
\[ \text{where: } \hat{p} = \text{proportion of inaccurate orders}, \]
\[ x = \text{number of inaccurate orders}, \]
\[ n = \text{total number of orders}. \]
### Part (b): Analyzing and Comparing the Intervals
**Choose the correct answer from the given options:**
- **A.** Since the upper confidence limit of the interval for Restaurant B is higher than both the lower and upper confidence limits of the interval for Restaurant A, this indicates that Restaurant B has a significantly higher percentage of inaccurate orders than Restaurant A.
- **B.** The lower confidence limit of the interval for Restaurant B is higher than the lower confidence limit of the interval for Restaurant A and the upper confidence limit of the interval for Restaurant B is also higher than the upper confidence limit of the interval for Restaurant A. Therefore, Restaurant B has a significantly higher percentage of inaccurate orders than Restaurant A.
- **C.** Since the two confidence intervals overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.
- **D.** No conclusion can be made because not enough information is given about the confidence interval for Restaurant B.
### Answer Analysis
Based on the given intervals:
- The confidence interval for Restaurant B is provided as 0.202 to 0.303.
- By comparing this interval to the one calculated for Restaurant A, conclusions can be drawn regarding the accuracy of the orders.
**
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