A medical doctor is interested in determining whether mean body temperatures are different in the morning and at night. Five patients were recruited and their body temperatures were measured first at 8 AM and then again at 10 PM. The data is in the following table: Patient 1 3 4 Morning Night 98.0 97.6 97.2 97.0 98.0 97.0 98.8 97.6 97.7 98.8 For this matched pairs experiment, you should take the differences by calculating: Morning - Night. What is the alternative hypothesis of interest?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Investigating Body Temperature Variations: A Matched Pairs Experiment
A medical doctor is investigating whether mean body temperatures differ between morning and night. Five patients participated in this study, and their body temperatures were recorded at 8 AM and again at 10 PM. The data are shown in the table below:
| Patient | Morning (°F) | Night (°F) |
|---------|--------------|------------|
| 1 | 98.0 | 97.0 |
| 2 | 97.6 | 98.8 |
| 3 | 97.2 | 97.6 |
| 4 | 97.0 | 97.7 |
| 5 | 98.0 | 98.8 |
For this matched pairs experiment, the differences should be calculated by subtracting the Night temperature from the Morning temperature. The proposed alternative hypothesis for this study is:
\[ H_1 : \mu_D \neq 0 \]
This indicates an interest in determining whether there is a significant difference in mean temperatures between these two times of day.
- **Hypotheses Options:**
- \( H_1 : \mu_D < 0 \)
- \( H_1 : \mu_D > 0 \)
- \( \mathbf{H_1 : \mu_D \neq 0} \) (selected option)
This data is a part of a larger study presented on page 4 of 15 in the document.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7269c65d-b7b5-4fbf-8945-da94b0914ae2%2Ff30b3a89-a52e-4acb-afe9-45edef4bdf7a%2F0deldog_processed.jpeg&w=3840&q=75)
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