30) **Constructing Confidence Intervals for Mean Drive-Through Service Times****Objective:**We're going to construct a 95% confidence interval estimate of the mean drive-through service time for two fast food restaurants, Restaurant X and Restaurant Y, during dinner time. Once we have calculated the intervals, we will compare the results.**Instructions:**1. Refer to the accompanying data set of mean drive-through service times at dinner in seconds for the two fast food restaurants.2. Construct a 95% confidence interval estimate of the mean drive-through service time for Restaurant X at dinner.3. Then, construct the same for Restaurant Y.4. Compare the results.**Procedure:****Step 1: Data Access** - Click the icon provided to view the data on drive-through service times.**Step 2: Construct Confidence Interval for Restaurant X** - Use the formula for the confidence interval: \(\bar{X} \pm t_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right)\) - where \(\bar{X}\) is the sample mean, \(t_{\alpha/2}\) is the t-score for a 95% confidence level, \(s\) is the sample standard deviation, and \(n\) is the sample size. - Insert these values into the formula to calculate the interval.**Representation:** - Fill in the boxes with the calculated values. - \[\text{Lower bound} \ < \ \mu \ < \ \text{Upper bound}\] - (Round to one decimal place as needed.)**Example:**\[130.2 \ < \ \mu \ < \ 150.6\]**Step 3: Repeat for Restaurant Y** - Follow the same procedure to calculate the confidence interval for Restaurant Y.**Step 4: Compare Intervals** - After constructing the intervals for both Restaurant X and Restaurant Y, analyze the intervals to see which restaurant has a more consistent (narrower interval) and quicker (lower average) service time.By following these steps, you will better understand the variability and performance of the drive-through service times for these two fast food restaurants. ### Restaurant Drive-Through Service TimesThe table below presents the service times (in seconds) for two different restaurants, Restaurant X and Restaurant Y.**Service Times (seconds)**| Restaurant X | Restaurant Y ||--------------|--------------|| 86 | 104 || 184 | 122 || 120 | 149 || 119 | 118 || 120 | 174 || 157 | 208 || 153 | 120 || 148 | 126 || 108 | 131 || 153 | 132 || 135 | 137 || 137 | 231 || 244 | 216 || 208 | 296 || 232 | 130 || 244 | 92 || 181 | 137 || 152 | 248 || 149 | 126 || 199 | 62 || 170 | 145 || 149 | 153 || 184 | 140 || 173 | 190 || 117 | 169 || 234 | 159 || 108 | 134 || 170 | 165 || 117 | 136 || 149 | 166 || 108 | 156 || 180 | 237 || 357 | 126 || 238 | 248 || 233 | 237 || 205 | 231 || 206 | 64 || 195 | 84 || 80 | 101 || 192 | 57 || 173 | 175 || 109 | 72 || 147 | 148 || 172 | 101 || 60 | 100 || 180 | 128 || 167 | 72 || 72 | 148 || 148 | 183 || 167 | 183 ||

Given is a dataset that provides the mean drive-through service times at dinner for two fast food…

Refer to the accompanying data set of mean drive-through service times at dinner in seconds at two fast food restaurants. Construct a 95% confidence interval estimate of the mean drive-through service time for Restaurant X at dinner; then do the same for Restaurant Y. Compare the results. Click the icon to view the data on drive-through service times. Construct a 95% confidence interval of the mean drive-through service times at dinner for Restaurant X. sec<μ< sec (Round to one decimal place as needed.)

Refer to the accompanying data set of mean drive-through service times at dinner in seconds at two fast food restaurants. Construct a 95% confidence interval estimate of the mean drive-through service time for Restaurant X at dinner; then do the same for Restaurant Y. Compare the results. Click the icon to view the data on drive-through service times. Construct a 95% confidence interval of the mean drive-through service times at dinner for Restaurant X. sec<μ< sec (Round to one decimal place as needed.)

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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Question

30)

**Constructing Confidence Intervals for Mean Drive-Through Service Times**

**Objective:**
We're going to construct a 95% confidence interval estimate of the mean drive-through service time for two fast food restaurants, Restaurant X and Restaurant Y, during dinner time. Once we have calculated the intervals, we will compare the results.

**Instructions:**
1. Refer to the accompanying data set of mean drive-through service times at dinner in seconds for the two fast food restaurants.
2. Construct a 95% confidence interval estimate of the mean drive-through service time for Restaurant X at dinner.
3. Then, construct the same for Restaurant Y.
4. Compare the results.

**Procedure:**

**Step 1: Data Access**
- Click the icon provided to view the data on drive-through service times.

**Step 2: Construct Confidence Interval for Restaurant X**
- Use the formula for the confidence interval: \(\bar{X} \pm t_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right)\)
- where \(\bar{X}\) is the sample mean, \(t_{\alpha/2}\) is the t-score for a 95% confidence level, \(s\) is the sample standard deviation, and \(n\) is the sample size.
- Insert these values into the formula to calculate the interval.

**Representation:**
- Fill in the boxes with the calculated values.
- \[\text{Lower bound} \ < \ \mu \ < \ \text{Upper bound}\]
- (Round to one decimal place as needed.)

**Example:**
\[
130.2 \ < \ \mu \ < \ 150.6
\]

**Step 3: Repeat for Restaurant Y**
- Follow the same procedure to calculate the confidence interval for Restaurant Y.

**Step 4: Compare Intervals**
- After constructing the intervals for both Restaurant X and Restaurant Y, analyze the intervals to see which restaurant has a more consistent (narrower interval) and quicker (lower average) service time.

By following these steps, you will better understand the variability and performance of the drive-through service times for these two fast food restaurants.

### Restaurant Drive-Through Service Times

The table below presents the service times (in seconds) for two different restaurants, Restaurant X and Restaurant Y.

**Service Times (seconds)**

| Restaurant X | Restaurant Y |
|--------------|--------------|
| 86 | 104 |
| 184 | 122 |
| 120 | 149 |
| 119 | 118 |
| 120 | 174 |
| 157 | 208 |
| 153 | 120 |
| 148 | 126 |
| 108 | 131 |
| 153 | 132 |
| 135 | 137 |
| 137 | 231 |
| 244 | 216 |
| 208 | 296 |
| 232 | 130 |
| 244 | 92 |
| 181 | 137 |
| 152 | 248 |
| 149 | 126 |
| 199 | 62 |
| 170 | 145 |
| 149 | 153 |
| 184 | 140 |
| 173 | 190 |
| 117 | 169 |
| 234 | 159 |
| 108 | 134 |
| 170 | 165 |
| 117 | 136 |
| 149 | 166 |
| 108 | 156 |
| 180 | 237 |
| 357 | 126 |
| 238 | 248 |
| 233 | 237 |
| 205 | 231 |
| 206 | 64 |
| 195 | 84 |
| 80 | 101 |
| 192 | 57 |
| 173 | 175 |
| 109 | 72 |
| 147 | 148 |
| 172 | 101 |
| 60 | 100 |
| 180 | 128 |
| 167 | 72 |
| 72 | 148 |
| 148 | 183 |
| 167 | 183 |
|

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