MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:The text describes a study conducted at a fast-food restaurant to evaluate a new drive-through system designed to reduce wait times. The existing mean waiting time is 84.4 seconds. The manager tests the new system by measuring wait times for 10 randomly selected orders. The recorded times are:
- 103.4
- 82.1
- 66.1
- 93.2
- 58.5
- 86.1
- 74.2
- 72.6
- 66.1
- 87.7
**Hypotheses:**
- Null hypothesis (\(H_0\)): The mean wait time is 84.4 seconds.
- Alternative hypothesis (\(H_1\)): The mean wait time is less than 84.4 seconds.
**Task:**
1. **Find the Test Statistic (\(t_0\)):**
- Round to two decimal places as needed.
2. **Find the P-value:**
- Round to three decimal places as needed.
3. **Conclusion Using Significance Level \( \alpha = 0.1 \):**
Choose from the following options:
- **A.** The P-value is less than the level of significance, so there is sufficient evidence to conclude the new system is effective.
- **B.** The P-value is greater than the level of significance, so there is not sufficient evidence to conclude the new system is effective.
- **C.** The P-value is less than the level of significance, so there is not sufficient evidence to conclude the new system is effective.
- **D.** The P-value is greater than the level of significance, so there is sufficient evidence to conclude the new system is effective.
Transcribed Image Text:The text provided is part of an educational exercise involving hypothesis testing and the analysis of waiting times at a fast-food restaurant. A manager believes a new drive-through system will reduce wait times, and data from 10 orders are provided for analysis.
**Table of Wait Times (in seconds):**
- 103.4, 82.1
- 66.1, 93.2
- 58.5, 86.1
- 74.2, 72.6
- 66.1, 87.7
**Analysis Steps:**
### (a) Verification of Conditions
- **Objective:** Verify that wait times are normally distributed and free of outliers.
- **Data Check:** A normal probability plot is provided with a sample correlation coefficient \( r = 0.989 \).
- **Analysis:**
- **Conditions Satisfied?** The text prompts to check two conditions using drop-down selections.
- **Interpretation of Plot:** The probability plot is described as linear enough due to the high correlation coefficient (\( r = 0.989 \)).
- **Boxplot:** No outliers are present.
### (b) Hypothesis Testing for System Effectiveness
- **Objective:** Determine if the new system effectively reduces wait times using the P-value approach at a significance level \(\alpha = 0.1\).
- **Hypotheses Setup:**
- Null Hypothesis (\( H_0 \)): \(\mu = 84.4\)
- Alternative Hypothesis (\( H_1 \)): \(\mu < 84.4\)
- **Task:** Find the test statistic using the provided options.
**Graph Explanation:**
- **Normal Probability Plot:** This graph plots expected z-scores against actual time data, showing a linear trend which supports normal distribution.
This exercise involves statistical understanding to determine the effectiveness of operational changes in reducing service times.
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