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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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### Customer Waiting Time Analysis

#### Overview
Understanding customer waiting times is essential to improving service efficiency and enhancing customer satisfaction. The data below presents the relationship between the number of customers and the waiting time in minutes.

#### Data Table

| Number of Customers | Waiting Time (Minutes) |
|---------------------|------------------------|
| 5 | 47 |
| 2 | 27 |
| 4 | 36 |
| 4 | 44 |
| 6 | 52 |
| 3 | 21 |
| 7 | 82 |
| 3 | 43 |
| 8 | 69 |
| 4 | 28 |

#### Key Observations
1. **Variation in Waiting Time**: As observed, waiting times range substantially from 21 minutes to 82 minutes.
2. **Customer Impact**: The data seems to suggest that the waiting time does not consistently increase or decrease with the number of customers. For instance, 4 customers resulted in varying waiting times (36, 44, and 28 minutes).
3. **Maximum and Minimum Waiting Times**: The maximum waiting time recorded is 82 minutes for 7 customers, while the minimum waiting time is 21 minutes for 3 customers.

#### Conclusion
This data can help businesses identify patterns and improve waiting times for better customer satisfaction. Further statistical analysis may be required to uncover more detailed trends and correlations.

$### Exercise 14.35 (Using the Estimated Regression Equation for Estimation and Prediction) Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, no-shows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system (pressherald.com). However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their name on the waiting list. The file *RestaurantLine* contains 10 observations of number of people in line ahead of a customer (independent variable $ x $) and actual waiting time (dependent variable $ y $). The estimated regression equation is: \[ \hat{y} = 4.35 + 8.81x \] and \[ \text{MSE} = 94.4236 \] Click on the datafile logo to reference the data. #### Instructions: Use [Table 2 of Appendix B](#) to solve the following: **a. Develop a point estimate for a customer who arrives with three people on the wait-list (to 1 decimal).** \[ \boxed{30.8} \text{ minutes} \] **b. Develop a 95% confidence interval for the mean waiting time for a customer who arrives with three customers already in line (to 2 decimals).** \[ \boxed{21.302} \text{ minutes}, \ \boxed{40.297} \text{ minutes} \] **c. Develop a 95% prediction interval for Roger and Sherry Davy's waiting time if there are three customers in line when they arrive (to 2 decimals).** \[ \boxed{6.43} \text{ minutes}, \ \boxed{55.17} \text{ minutes} \] **d. Discuss the differences in your answers to parts (b) and (c).** The prediction interval is $\boxed{\text{wider}}$ than the confidence interval. #### Explanation of Graphs/Diagrams: The document does not include any graphs or diagrams. However, it provides numerical results for point estimates, confidence intervals, and prediction intervals related to waiting times based on a regression model for customers arriving at a restaurant with a certain number of people already in line. **Note:** The "Hide Feedback" and "Partially Correct" boxes at the bottom indicate an option available during$

Transcribed Image Text:### Exercise 14.35 (Using the Estimated Regression Equation for Estimation and Prediction) Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, no-shows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system (pressherald.com). However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their name on the waiting list. The file *RestaurantLine* contains 10 observations of number of people in line ahead of a customer (independent variable $ x $) and actual waiting time (dependent variable $ y $). The estimated regression equation is: \[ \hat{y} = 4.35 + 8.81x \] and \[ \text{MSE} = 94.4236 \] Click on the datafile logo to reference the data. #### Instructions: Use [Table 2 of Appendix B](#) to solve the following: **a. Develop a point estimate for a customer who arrives with three people on the wait-list (to 1 decimal).** \[ \boxed{30.8} \text{ minutes} \] **b. Develop a 95% confidence interval for the mean waiting time for a customer who arrives with three customers already in line (to 2 decimals).** \[ \boxed{21.302} \text{ minutes}, \ \boxed{40.297} \text{ minutes} \] **c. Develop a 95% prediction interval for Roger and Sherry Davy's waiting time if there are three customers in line when they arrive (to 2 decimals).** \[ \boxed{6.43} \text{ minutes}, \ \boxed{55.17} \text{ minutes} \] **d. Discuss the differences in your answers to parts (b) and (c).** The prediction interval is $\boxed{\text{wider}}$ than the confidence interval. #### Explanation of Graphs/Diagrams: The document does not include any graphs or diagrams. However, it provides numerical results for point estimates, confidence intervals, and prediction intervals related to waiting times based on a regression model for customers arriving at a restaurant with a certain number of people already in line. **Note:** The "Hide Feedback" and "Partially Correct" boxes at the bottom indicate an option available during

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