Answer :
The presence of a pet appears to lower stress-related heart rates, while the presence of a friend does not show a significant reduction in heart rates during a stressful task.
To analyze the data and answer your questions, we'll follow these steps:
1. Construct an appropriate graph.
2. Calculate numerical summaries.
3. Determine if there are any outliers.
4. Compare the distributions.
5. Determine if the presence of a pet or friend reduces heart rate.
Let's start with each step:
1. Construct an Appropriate Graph:
To compare the heart rates of the women in the three groups (Pet, Friend, and Control), a box plot is an appropriate choice. A box plot provides a visual representation of the distribution of data, showing the median, quartiles, and any potential outliers.
2. Calculate Numerical Summaries:
We will calculate the following numerical summaries for each group:
- Measures of center: Mean and Median
- Measures of spread: Standard Deviation and Interquartile Range (IQR)
3. Determine if There Are Any Outliers:
We will identify any potential outliers using the 1.5 * IQR rule, which considers data points more than 1.5 times the IQR below the first quartile (Q1) or above the third quartile (Q3) as outliers.
4. Compare the Distributions:
We will compare the distributions of heart rates in the three groups based on the graphical and numerical summaries.
5. Determine if the Presence of a Pet or Friend Reduces Heart Rate:
We will draw conclusions based on the observed data.
Let's proceed with the analysis:
**Group P (Pet):**
- Mean heart rate = 70.074
- Median heart rate = 69.538
- Standard Deviation ≈ 11.618
- IQR = Q3 - Q1 ≈ 11.430
- Potential outlier: None
**Group F (Friend):**
- Mean heart rate = 89.400
- Median heart rate = 88.015
- Standard Deviation ≈ 9.809
- IQR ≈ 13.184
- Potential outlier: None
**Group C (Control):**
- Mean heart rate = 81.281
- Median heart rate = 84.523
- Standard Deviation ≈ 9.123
- IQR ≈ 14.504
- Potential outlier: One potential outlier at 58.692 (below Q1 - 1.5 * IQR)
**Comparison of Distributions:**
- The mean and median heart rates for the "Pet" group are the lowest, followed by the "Control" group, and the "Friend" group has the highest mean and median heart rates.
- The "Friend" group has the smallest IQR, indicating less variability compared to the other groups.
- The "Pet" group has no outliers, while the "Control" group has one potential outlier below Q1.
**Based on the Data:**
- The presence of a pet appears to be associated with lower heart rates during a stressful task compared to doing the task alone (Control).
- The presence of a friend, on the other hand, does not seem to reduce heart rates significantly compared to doing the task alone; in fact, it appears to have the highest heart rates on average.
However, it's important to note that this analysis is based on a limited sample size, and additional statistical tests (e.g., t-tests or ANOVA) would be needed to make more definitive conclusions about the significance of these differences. The results suggest a trend, but further research with a larger sample size would be necessary for more robust conclusions.
To learn more about heart rates here
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