HW Score: 41.85%, 3.77 of 9 pts & 7.1.19-T Question Help ▼ In a study of the accuracy of fast food drive-through orders, Restaurant A had 248 accurate orders and 56 that were not accurate. a. Construct a 90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.171
HW Score: 41.85%, 3.77 of 9 pts & 7.1.19-T Question Help ▼ In a study of the accuracy of fast food drive-through orders, Restaurant A had 248 accurate orders and 56 that were not accurate. a. Construct a 90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.171
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Study of Fast Food Drive-Through Order Accuracy**
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**Question 7.1.19-T**
In a study of the accuracy of fast food drive-through orders, Restaurant A had 248 accurate orders and 56 that were not accurate.
**Instructions:**
- **a.** Construct a 90% confidence interval estimate of the percentage of orders that are not accurate.
- **b.** Compare the results from part **(a)** to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B: \(0.171 < p < 0.239\). What do you conclude?
---
**Solution:**
**a. Construct a 90% confidence interval. Express the percentages in decimal form.**
\[ 0.148 < p < 0.221 \]
(Round to three decimal places as needed.)
---
**Explanation:**
1. **Data for Restaurant A:**
- Accurate orders: 248
- Inaccurate orders: 56
- Total orders: 304
2. **Calculation of Proportion of Inaccurate Orders in Restaurant A:**
\[ \hat{p} = \frac{56}{304} \approx 0.184 \]
3. **Standard Error (SE):**
\[ SE = \sqrt{\frac{\hat{p} \cdot (1 - \hat{p})}{n}} = \sqrt{\frac{0.184 \cdot (1 - 0.184)}{304}} \approx 0.023 \]
4. **Margin of Error (ME) for 90% Confidence Level (Z \approx 1.645):**
\[ ME = Z \cdot SE = 1.645 \cdot 0.023 \approx 0.038 \]
5. **Confidence Interval:**
\[ \hat{p} - ME < p < \hat{p} + ME \]
\[ 0.184 - 0.038 < p < 0.184 + 0.038 \]
\[ 0.148 < p < 0.221 \]
---
**b. Comparison with Restaurant B:**
- Restaurant B's confidence interval: \(0.171 < p < 0.239\)
- Restaurant A's confidence interval: \(0.148 < p < 0.221\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f4a9f05-fdd6-4e90-876c-ee547117be59%2Fcd2f0af3-e2bd-4b86-a39c-7b5d83e24393%2Fxca01x9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Study of Fast Food Drive-Through Order Accuracy**
---
**Question 7.1.19-T**
In a study of the accuracy of fast food drive-through orders, Restaurant A had 248 accurate orders and 56 that were not accurate.
**Instructions:**
- **a.** Construct a 90% confidence interval estimate of the percentage of orders that are not accurate.
- **b.** Compare the results from part **(a)** to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B: \(0.171 < p < 0.239\). What do you conclude?
---
**Solution:**
**a. Construct a 90% confidence interval. Express the percentages in decimal form.**
\[ 0.148 < p < 0.221 \]
(Round to three decimal places as needed.)
---
**Explanation:**
1. **Data for Restaurant A:**
- Accurate orders: 248
- Inaccurate orders: 56
- Total orders: 304
2. **Calculation of Proportion of Inaccurate Orders in Restaurant A:**
\[ \hat{p} = \frac{56}{304} \approx 0.184 \]
3. **Standard Error (SE):**
\[ SE = \sqrt{\frac{\hat{p} \cdot (1 - \hat{p})}{n}} = \sqrt{\frac{0.184 \cdot (1 - 0.184)}{304}} \approx 0.023 \]
4. **Margin of Error (ME) for 90% Confidence Level (Z \approx 1.645):**
\[ ME = Z \cdot SE = 1.645 \cdot 0.023 \approx 0.038 \]
5. **Confidence Interval:**
\[ \hat{p} - ME < p < \hat{p} + ME \]
\[ 0.184 - 0.038 < p < 0.184 + 0.038 \]
\[ 0.148 < p < 0.221 \]
---
**b. Comparison with Restaurant B:**
- Restaurant B's confidence interval: \(0.171 < p < 0.239\)
- Restaurant A's confidence interval: \(0.148 < p < 0.221\
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