105.3 79.0 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 84.7 seconds. A manager devises a new drive-through system that he believes will decrease wait time. As a test, he initiates the new system at his 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. 66.4 56.7 95.7 84.7 75.0 66.5 71.1 79.6 E 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= 0.981. Are the conditions for testing the hypothesis satisfied? Yes, the conditions satisfied. The normal probability plot is linear enough, since the correlation coefficient is AExpected z-score Q are greater than the critical value. In addition, a boxplot does not show any outliers. 1- 0- 60 5 90 165 -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 = 0.01.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

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 84.7 seconds. A manager devises a new drive-through system that he believes will decrease wait time. As a test, he initiates the new system at his 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.

# Hypothesis Testing for Drive-Through Wait Times

The mean waiting time at a drive-through of a fast-food restaurant from the time an order is placed to the time the order is received is 84.7 seconds. A manager devises a new drive-through system that he believes will decrease wait time. As a test, he initiates the new system at his 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.

### Wait Times Data
| Time (sec) | Time (sec) |
|------------|------------|
| 105.3 | 79.0 |
| 66.4 | 95.7 |
| 56.7 | 84.7 |
| 75.0 | 71.1 |
| 66.5 | 79.6 |

## Part (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 = 0.981 $.

**Question:** Are the conditions for testing the hypothesis satisfied?

**Answer:**
- **Yes**, the conditions *are* satisfied. The normal probability plot *is* linear enough, since the correlation coefficient is *greater* than the critical value. In addition, a boxplot does not show any outliers.

#### Normal Probability Plot
The normal probability plot depicted shows observed data versus expected data (z-scores). The data points primarily follow a straight line, indicating that the data is approximately normally distributed.

## Part (b)
**Question:** Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of $ \alpha = 0.01 $.

### Hypotheses
\[
H_0: \mu = 84.7
\]
\[
H_1: \mu < 84.7
\]

### Calculation
1. **Find the test statistic:**
\[
t_0 = 78 \quad \text{(Round to two decimal places as needed.)}
\]

2. **Find the P-value:**

The P-value is \( 13.73 \quad \text{(Round to three decimal places as needed

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Research Ethics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions