Introduction

We used a data set from a paper “A critical appraisal of 98.6 degrees F, the upper limit of the normal body temperature, and other legacies of Carl Reinhold August Wunderlich” published in the Journal of the American Medical Association 268: 1578-1580 by Mackowiak, P.A., Wasserman, S.S., and Levine, M.M. in 1992. The data set is available as HumanBodyTemp in the abd package. In this data set, it contains the body termperature for 25 randomly chosen health people.

data("HumanBodyTemp")
View(HumanBodyTemp)
help("HumanBodyTemp")

It is known that the internal human body temperature is 98.6 degrees F. (See https://en.wikipedia.org/wiki/Human_body_temperature) We are interested to see if this is reaonable or not. Below is our research question:

Is it reasonable to say that the average human body temperature is 98.6 degrees F?

Methods

The 25 individuals of the “HumanBodyTemp” data frame are as follows:

head(HumanBodyTemp,25)
##     temp
## 1   98.4
## 2   98.6
## 3   97.8
## 4   98.8
## 5   97.9
## 6   99.0
## 7   98.2
## 8   98.8
## 9   98.8
## 10  99.0
## 11  98.0
## 12  99.2
## 13  99.5
## 14  99.4
## 15  98.4
## 16  99.1
## 17  98.4
## 18  97.6
## 19  97.4
## 20  97.5
## 21  97.5
## 22  98.8
## 23  98.6
## 24 100.0
## 25  98.4

The variable involved in the research question is temperature and it is numerical. To see if it is reasonable to say that the average human body temperature is 98.6 degrees F, we analyzed the data. First, we analyzed the data with a density plot. The density plot gave us an idea for what our 95% confidence interval range is going to look like. We also looked at numerical data, such as the mean and median of the data. The mean will give us our X-Bar of the data (the sample data mean). We will use a ttest code to find the estimate of mu and SE. We will also be able to find our lower bound and upper bound of the interval and the test statistic, degree of freedom, and the P-value.

Results

First, we will look at the descriptive results we concluded.

Descriptive Results

The two types of descriptive results we will look at are graphical descriprive results and numerical descriptive results.

Graphical Descriptive Results

densityplot(~temp,data=HumanBodyTemp,xlab="Degrees Fahrenheit", main="Temperature")

The density plot provides a unimodel symmetric, bell shaped, graph. The graph peaks between 98 and 99. This tells us that there is going some variance in temperature, but a strong average towards the 98 and 99 area. Based on this observation, I think the sample mean is close to 98.6.

Numerical Descriptive Results

The numerical data can provide us with the baseline of our information that can confirm our hypothesis.

favstats(~temp,data=HumanBodyTemp)
##   min Q1 median Q3 max   mean        sd  n missing
##  97.4 98   98.6 99 100 98.524 0.6777905 25       0

The data shows that the mean of the body temperatures is 98.524, our standard deviation is 0.68, and our median is 98.6. This shows how, on average, the temperatures were 98.524 degrees fahrenheit, and had a small variance to them. The median shows the center of our data, 98.6.

Inferential Results

Our null hypothesis is \(H_0\):=98.6

Our alternative hypothesis is \(H_a\):≠98.6

ttestGC(~temp,data=HumanBodyTemp,mu=98.6,alternative="two.sided")
## 
## 
## Inferential Procedures for One Mean mu:
## 
## 
## Descriptive Results:
## 
## variable  mean     sd       n          
## temp      98.524   0.678    25         
## 
## 
## Inferential Results:
## 
## Estimate of mu:   98.52 
## SE(x.bar):    0.1356 
## 
## 95% Confidence Interval for mu:
## 
##           lower.bound         upper.bound          
##           98.244222           98.803778            
## 
## Test of Significance:
## 
##  H_0:  mu = 98.6 
##  H_a:  mu != 98.6 
## 
##  Test Statistic:     t = -0.5606 
##  Degrees of Freedom:   24 
##  P-value:        P = 0.5802

This data provided us with the 95% confidence intervals for our hypothesis. The 95% confidence interval is between 98.244222 and 98.803778. Confidence interval is a range that states the mean average sits between because of the information provided in our sample. We are 95% confident that the average human body temperature is somewhere between 98.244222 degrees Fahrenheit and 98.803778 degrees Fahrenheit. It also shows us our consistency within our data through the p-value. Because the p-value (0.5802) is greater than the significance level 0.05, we can accept our null hypothesis that the average human body temperature is equal to 98.6 degrees F.

Discussion and Conclusion

The mean of the body temperatures is 98.524, our standard deviation is 0.68, and our median is 98.6. This shows how, on average, the temperatures were 98.524 degrees fahrenheit, and had a small variance to them. The median shows the center of our data, 98.6. Because the p-value (0.5802) is greater than the significance level 0.05, we can accept our null hypothesis, therefore the average human body temperature is equal to 98.6 degrees F.