Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d and s4. In general, what does u, represent? Temperature (F) at 8 AM Temperature (°F) at 12 AM 98.5 97.9 99.4 97.5 97.8 97.7 D 99.7 97.9 97.5 98.0 Let the temperature at 8 AM be the first sample, and the temperature at 12AM be the second sample. Find the values of d and s. d= -0.26 (Type an integer or a decimal. Do not round.) (Round to two decimal places as needed.)

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**Title: Analysis of Body Temperature Variations**

**Overview:**

This study involves the recording of body temperatures from five different subjects at two different time points: 8 AM and 12 AM. The goal is to calculate the mean difference (\( \bar{d} \)) and the standard deviation of the differences (\( s_d \)) between these two samples. Additionally, this analysis seeks to understand what \( \mu_d \) generally represents.

**Data Table:**

| Time          | Subject 1 | Subject 2 | Subject 3 | Subject 4 | Subject 5 |
|---------------|-----------|-----------|-----------|-----------|-----------|
| Temperature (°F) at 8 AM  | 97.9      | 99.4      | 97.5      | 97.8      | 97.7      |
| Temperature (°F) at 12 AM | 98.5      | 99.7      | 97.9      | 97.5      | 98.0      |

**Tasks:**

1. **Mean Difference (\( \bar{d} \)):**
   - The value of \( \bar{d} \) is given as \(-0.26\).
   - \( \bar{d} \) represents the average difference in temperatures from 8 AM to 12 AM across all subjects.

2. **Standard Deviation of Differences (\( s_d \)):**
   - The value of \( s_d \) is to be calculated and should be rounded to two decimal places.
   - \( s_d \) signifies the variability or spread of the differences between the two time points across all subjects.

**Explanation of \( \mu_d \):**

\( \mu_d \) represents the mean difference of the entire population from which the sample is drawn. It is a population parameter that indicates the expected average change in temperature between the two time points for all similar subjects.

**Conclusion:**

This study aids in comprehending temperature fluctuations within individuals over a specified time. The values of \( \bar{d} \) and \( s_d \) provide insight into average trends and variability, respectively, which can be essential for health assessments or other scientific explorations.
Transcribed Image Text:**Title: Analysis of Body Temperature Variations** **Overview:** This study involves the recording of body temperatures from five different subjects at two different time points: 8 AM and 12 AM. The goal is to calculate the mean difference (\( \bar{d} \)) and the standard deviation of the differences (\( s_d \)) between these two samples. Additionally, this analysis seeks to understand what \( \mu_d \) generally represents. **Data Table:** | Time | Subject 1 | Subject 2 | Subject 3 | Subject 4 | Subject 5 | |---------------|-----------|-----------|-----------|-----------|-----------| | Temperature (°F) at 8 AM | 97.9 | 99.4 | 97.5 | 97.8 | 97.7 | | Temperature (°F) at 12 AM | 98.5 | 99.7 | 97.9 | 97.5 | 98.0 | **Tasks:** 1. **Mean Difference (\( \bar{d} \)):** - The value of \( \bar{d} \) is given as \(-0.26\). - \( \bar{d} \) represents the average difference in temperatures from 8 AM to 12 AM across all subjects. 2. **Standard Deviation of Differences (\( s_d \)):** - The value of \( s_d \) is to be calculated and should be rounded to two decimal places. - \( s_d \) signifies the variability or spread of the differences between the two time points across all subjects. **Explanation of \( \mu_d \):** \( \mu_d \) represents the mean difference of the entire population from which the sample is drawn. It is a population parameter that indicates the expected average change in temperature between the two time points for all similar subjects. **Conclusion:** This study aids in comprehending temperature fluctuations within individuals over a specified time. The values of \( \bar{d} \) and \( s_d \) provide insight into average trends and variability, respectively, which can be essential for health assessments or other scientific explorations.
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