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The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 87.5 seconds. A manager devises a new drive-through system that she believes will decrease wait time. As a test, she initiates the new system at her restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts (a) and (b) below. 103.2 80.8 66.9 93.3 56.1 86.1 74.4 69.7 64.1 85.4 Click the icon to view the table of correlation coefficient critical values. (a) Because the sample size is small, the manager must verify that the wait time is normally distributed and the sample does not contain any outliers. The normal probability plot is shown below and the sample correlation coefficient is known to be r=0.993. Are the conditions for testing the hypothesis satisfied? satisfied. The normal probability plot the conditions show any outliers. linear enough, since the correlation coefficient is than the critical value. In addition, a boxplot does not A Expected 2-score 2 1. 0- OFFET 1gb hd -1- Time (sec) (b) is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of a = 0.05. First determine the appropriate hypotheses. o S

The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 87.5 seconds. A manager devises a new drive-through system that she believes will decrease wait time. As a test, she initiates the new system at her restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts (a) and (b) below. 103.2 80.8 66.9 93.3 56.1 86.1 74.4 69.7 64.1 85.4 Click the icon to view the table of correlation coefficient critical values. (a) Because the sample size is small, the manager must verify that the wait time is normally distributed and the sample does not contain any outliers. The normal probability plot is shown below and the sample correlation coefficient is known to be r=0.993. Are the conditions for testing the hypothesis satisfied? satisfied. The normal probability plot the conditions show any outliers. linear enough, since the correlation coefficient is than the critical value. In addition, a boxplot does not A Expected 2-score 2 1. 0- OFFET 1gb hd -1- Time (sec) (b) is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of a = 0.05. First determine the appropriate hypotheses. o S

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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**Evaluating the Effectiveness of a New Drive-Through System at a Fast-Food Restaurant** **Introduction** The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 87.5 seconds. A manager devises a new drive-through system that she believes will decrease wait time. As a test, she initiates the new system at her restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table below. Complete parts (a) and (b) below. | Wait Times (seconds) | |------------------------| | 103.2 | 80.8 | | 66.9 | 93.3 | | 56.1 | 86.1 | | 74.4 | 69.7 | | 64.1 | 85.4 | **(a) Verification of Normality and Outliers** Because the sample size is small, the manager must verify that the wait time is normally distributed and the sample does not contain any outliers. The normal probability plot is shown below and the sample correlation coefficient is known to be \( r = 0.993 \). **Conditions to Test the Hypothesis:** - **Normal Probability Plot and Correlation Coefficient:** - The normal probability plot should be linear enough. - The sample correlation coefficient should be compared to the critical value. - **Outliers:** - A box plot should not show any outliers. ![Expected z-score vs Time (sec)](expected_z_score_plot.png) - The normal probability plot provided indicates linearity since the dots roughly follow a straight line. **Question: Are the conditions for testing the hypothesis satisfied?** - **Conditions Satisfied:** Yes, the conditions are satisfied. - **Linearity of Normal Probability Plot:** The normal probability plot is linear enough. - **Comparison with Critical Value:** The correlation coefficient is greater than the critical value. - **Boxplot Analysis:** A boxplot does not show any outliers. **(b) Hypothesis Testing** **Is the new system effective?** Conduct a hypothesis test using the P-value approach and a level of significance of \( \alpha = 0.05 \). **Steps:** 1. **Determine the Hypotheses:** - Null Hypothesis (\(H_0
Transcribed Image Text:**Evaluating the Effectiveness of a New Drive-Through System at a Fast-Food Restaurant** **Introduction** The mean waiting time at the drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 87.5 seconds. A manager devises a new drive-through system that she believes will decrease wait time. As a test, she initiates the new system at her restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table below. Complete parts (a) and (b) below. | Wait Times (seconds) | |------------------------| | 103.2 | 80.8 | | 66.9 | 93.3 | | 56.1 | 86.1 | | 74.4 | 69.7 | | 64.1 | 85.4 | **(a) Verification of Normality and Outliers** Because the sample size is small, the manager must verify that the wait time is normally distributed and the sample does not contain any outliers. The normal probability plot is shown below and the sample correlation coefficient is known to be \( r = 0.993 \). **Conditions to Test the Hypothesis:** - **Normal Probability Plot and Correlation Coefficient:** - The normal probability plot should be linear enough. - The sample correlation coefficient should be compared to the critical value. - **Outliers:** - A box plot should not show any outliers. ![Expected z-score vs Time (sec)](expected_z_score_plot.png) - The normal probability plot provided indicates linearity since the dots roughly follow a straight line. **Question: Are the conditions for testing the hypothesis satisfied?** - **Conditions Satisfied:** Yes, the conditions are satisfied. - **Linearity of Normal Probability Plot:** The normal probability plot is linear enough. - **Comparison with Critical Value:** The correlation coefficient is greater than the critical value. - **Boxplot Analysis:** A boxplot does not show any outliers. **(b) Hypothesis Testing** **Is the new system effective?** Conduct a hypothesis test using the P-value approach and a level of significance of \( \alpha = 0.05 \). **Steps:** 1. **Determine the Hypotheses:** - Null Hypothesis (\(H_0
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