Survey Question solved using Analytics: Whether true mean body temperature is 98.6?

                 

Pandemics is a large-scale outbreaks of infectious disease that can greatly increase morbidity and mortality over a wide geographic area. There is significant gap and challenges exists in the global pandemic preparedness.
And its early sign of symptoms includes FEVER.

This FEVER, raised the question regarding the notion of true mean        body temperature 98.6. Whether to considered for both men and women  as same? Is this temperature an ideal for everyone?Whether we at risk? What is the true mean body temperature?

An article was written on Journal of the American Medical Association in 1992. They did survey on 65 males and 65 females to check whether the mean body temperature of female is same as for male. Based on this survey, this generalize the same pattern among overall population.

Today, using the power of statistics this problem can be addressed. 

Here, the data based on the survey itself.

Let's get started with the analysis of data....😅

The data description as follows:  

# Id: 

# Body Temperature 

# Gender 

# Heart Rate

Numerical Variables: body_temperature,heart_rate

Categorical Variables: Gender

Glimpse of data: first 10 observations out of 130 observations.

Steps*:
  
Firstly, need to find the distribution of data, to check whether data is normally distributed or not?
Drilling down w.r.t the continuous variable, need to figure out the mean, the standard deviation and the spread of data.
Secondly, performing t-test to determine whether the mean temperature of body is 98.6. Producing confidence interval plot of Body temperature. 

Code Snipet:

%let interval=BodyTemp HeartRate;

proc univariate data=temp noprint;

    var &interval;

    histogram &interval / normal kernel;

    inset n mean std / position=ne;

    title "Interval Variable Distribution Analysis";

run;

title;

Blue colored curve shows the ideal bell shaped data distribution. This red curve looks identical to bell-shaped curve. i.e the distribution of BodyTemp.

N=130 which means no missing values.

Mean(μ) = 98.25

Standard Deviation(Stdev)=0.73

This red curve is quiet similarly resembles like a bell-shaped guassian curve.

N=130 which means no missing values.

Mean(μ) = 73.76

Standard Deviation(Stdev)=7.06

This depicts normal distribution of data.

To perform one-sample t test to determine the mean of body temperature is 98.6

Hypothesis Statement:
Null Hypothesis(H0): The mean body temperature is 98.6
Alternative Hypothesis(Ha): The mean body temperature is not 98.6


Code Snipet:

proc ttest data=temp h0=98.6

           plots(only shownull)=interval;

   var BodyTemp;

   title 'Testing Whether the Mean Body Temperature = 98.6';

run;

title;

From the above table, it clearly depicts that the range of temperature lies between 96.3 to 100.8 F.
According to 95% confidence interval, the average temperature will lies with 98.12 to 98.38.
Even, standard deviation does not show much variation in value. 
Here, alpha consider as 0.05

Degree of Freedom= N-1 =130-1=129
Here, p-value is highly significant. As p-value is low, we fail to accept the null hypothesis.

Therefore, the mean body temperature is not 98.6. 

From the above plot, confidence interval lies with the range of 98.1 to 98.4. So, 95% probability that the mean body temperature of any person must be within this range only.

According to this analysis, the true mean body temperature is 98.2 F.

Conclusion:
The average body temperature is 98.2 F But as per 95% confidence interval, your temperature might range between 98.1 F to 98.4 F. 
If your body temperature is beyond 98.4 F then you might got infected. 

Happy Learning 🙋😃