Q. 6.135 - Elementary Statistics

Question

A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans $98.6^{\circ }F$. the results of the study by P. Mackowiak et al. appeared in the article "A Critical Appraisal of $98.6^{\circ }F$, the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich". Among other data, the researchers obtained the body temperatures of $93$ healthy humans, as provided on the WeissStats site. Use the technology of your choice to do the following.

Part (a): Obtain a histogram of the data and use it to assess the normality of the variable under consideration.

Part (a): Obtain a normal probability plot of the data and use it to asses the normality of the variable under consideration.

Part (c): Compare your results in part (a) and (b).

Step-by-Step Solution

Answer

Part (a): The required histogram is given below,

Part (b): The normal probability plot is given below,

There are no outliers in the data.

The temperature is approximately normally distributed.

Part (c): Both the results in parts (a) and (b) are approximately the same.

Part (a) Step 1. Given information.

Consider the given question,

Part (a) Step 2. Draw a histogram of the data.

On plotting a histogram,

We have superimposed normal curve associated with the variable. The shape of the histogram is quite close to that of the normal curve, as we would expect because of the large number of observations.

Part (b) Step 1. Plot a normal probability plot of the data.

The graph given below is the normal probability plot of the variable temperature,

From the above plot, we can say observe that no observations fall outside the overall pattern of the data. So, there are no outliers in the data.

The plot is roughly linear. Hence, we can assume that the temperature is approximately normally distributed.

Part (c) Step 1. Compare the results in part (a) and (b).

On comparing the results in part (a) and (b),

Both the results are approximately the same.

This is due to the large sample size.