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**Case Study**

**Do Pets or Friends Help Reduce Stress?**

If you are a dog lover, having your dog with you may reduce your stress level. Does having a friend with you reduce stress? To examine the effect of pets and friends in stressful situations, researchers recruited 45 women who said they were dog lovers. Fifteen women were assigned at random to each of three groups: to do a stressful task alone, with a good friend present, or with their dogs present. The stressful task was to count backward by 13s or 17s. The woman’s average heart rate during the task was one measure of the effect of stress. The table below shows the data.

**Average heart rates during stress with a pet (P), with a friend (F), and for the control group (C)**

| Group | Rate | Group | Rate | Group | Rate | Group | Rate |
|-------|------|-------|------|-------|------|-------|------|
| P | 69.2 | P | 68.9 | C | 84.7 | C | 75.5 |
| F | 99.7 | C | 87.2 | C | 84.9 | C | 62.6 |
| P | 70.2 | P | 64.2 | P | 58.7 | P | 70.1 |
| C | 80.4 | C | 91.8 | P | 79.7 | F | 88.0 |
| C | 87.4 | C | 87.8 | P | 69.2 | F | 81.6 |
| P | 76.0 | F | 91.4 | C | 73.3 | F | 87.0 |
| F | 83.4 | F | 100.9| C | 84.5 | F | 92.5 |
| F | 102.2| C | 77.8 | C | 70.9 | P | 72.3 |
| P | 86.4 | P | 97.5 | F | 89.8 | P | 65.4 |
| F | 80.3 | P | 85.0 | F | 98.2 | | |
| C | 90.0 | F | 101.0| F | 76.9 | | |
| C | 99.0 | F | 97.0 | P | 69.5 | | |

1. **Construct an appropriate graph for comparing the heart rates of the women in the three groups.**

2. **Calculate numerical summaries for each group’s data. Which measures of center and variability would you choose to compare? Why?**

3. **Determine if there are any outliers in each of the three groups. Show your work.**

4. **Write a few sentences comparing the distributions of heart rates for the women in the three groups.**

5. **Based on the data, does it appear that the presence of a pet or friend reduces heart rate during a stressful task? Justify your answer.**

Answer :

Final answer:

To compare the heart rates of women in three groups with pets, friends, and alone, construct a graph, calculate numerical summaries to compare the groups, identify outliers, compare the distributions of heart rates, and determine if the presence of a pet or friend reduces heart rate.

Explanation:

1. Constructing the graph

To compare the heart rates of the women in the three groups, you can create a box plot for each group, with heart rate values as the data points. The x-axis will represent the three groups, and the y-axis will represent the heart rate values.

2. Calculating numerical summaries

To compare the heart rates, you can calculate measures of center and variability for each group. Mean and standard deviation can be used as the measures of center and variability, respectively, for comparing the heart rate data of the three groups.

3. Identifying outliers

To determine outliers in each group, you can use the interquartile range (IQR) method. Any data point that falls below the lower whisker or above the upper whisker in a box plot can be considered an outlier.

4. Comparing the distributions

The distributions of heart rates for the women in the three groups can be compared based on the shape, center, and spread of the box plots. The presence of outliers and the amount of overlap between the box plots can also be considered while comparing the distributions.

5. Determining the effect of pets or friends

Based on the data, you can compare the mean heart rates of each group to determine if the presence of a pet or friend reduces heart rate during a stressful task. If the mean heart rate is lower in the group with pets or friends compared to the group that does the task alone, it suggests that having a pet or friend reduces heart rate during a stressful task.

Learn more about Comparing heart rates with pets and friends here:

https://brainly.com/question/32328524

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