A study by researchers at the University of Maryland...

A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is $98.6^{\circ} \mathrm{F}$. The results of the study by P. Mackowiak et al. appeared in the article "A Critical Appraisal of $98.6^{\circ} \mathrm{F},$ the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich" (Journal of the American Medical Association, Vol. 268, pp. 1578-1580). Among other data, the researchers obtained the body temperatures of 93 healthy humans, as provided on the WeissStats CD. Use the technology of your choice to do the following. a. Obtain a normal probability plot, boxplot, histogram, and stem-and-leaf diagram of the data. b. Based on your results from part (a), can you reasonably apply one-standard-deviation $x^{2}$ -procedures to the data? Explain your reasoning. c. In Exercise 9.81. you were asked to use these data to decide whether mean body temperature of healthy humans differs from $98.6^{\circ} \mathrm{F}$. There, you were to assume that the population standard deviation of body temperatures for healthy humans is $0.63^{\circ} \mathrm{F}$. At the $5 \%$ significance level, do the data provide evidence against that assumption? d. Find and interpret a $95 \%$ confidence interval for the population standard deviation of body temperatures for healthy humans.

A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is $98.6^{\circ} \mathrm{F}$. The results of the study by P. Mackowiak et al. appeared in the article "A Critical Appraisal of $98.6^{\circ} \mathrm{F},$ the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich" (Journal
of the American Medical Association, Vol. 268, pp. 1578-1580). Among other data, the researchers obtained the body temperatures of 93 healthy humans, as provided on the WeissStats CD. Use the technology of your choice to do the following.
a. Obtain a normal probability plot, boxplot, histogram, and stem-and-leaf diagram of the data.
b. Based on your results from part (a), can you reasonably apply one-standard-deviation $x^{2}$ -procedures to the data? Explain your reasoning.
c. In Exercise 9.81. you were asked to use these data to decide whether mean body temperature of healthy humans differs from $98.6^{\circ} \mathrm{F}$. There, you were to assume that the population standard deviation of body temperatures for healthy humans is $0.63^{\circ} \mathrm{F}$. At the $5 \%$ significance level, do the data provide evidence against that assumption?
d. Find and interpret a $95 \%$ confidence interval for the population standard deviation of body temperatures for healthy humans.

Key Concepts

Exploratory Data Analysis (EDA)

Exploratory Data Analysis involves using visual tools such as histograms, boxplots, stem?and?leaf diagrams, and normal probability plots to summarize the main characteristics of a data set. These visualizations help in understanding the distribution, identifying outliers, checking for symmetry, and revealing patterns in the data, which is critical before performing any formal analyses or statistical tests.

Normality Assessment

Normality Assessment is the process of evaluating whether a data set approximates a normal distribution. Tools like the normal probability plot allow statisticians to visually inspect if the data points fall approximately along a straight line, which suggests that the assumptions of normality required for many inferential procedures, such as z-tests or t-tests, are tenable.

One-Standard-Deviation Procedures

One-Standard-Deviation Procedures refer to methods or rules that rely on the assumption of normality to define approximate thresholds for variability, such as considering data within one standard deviation from the mean to be typical under a normal distribution. Their appropriateness depends critically on the data actually following a normal distribution and on the absence of extreme outliers.

Hypothesis Testing

Hypothesis Testing is a statistical framework used to make decisions about population parameters based on sample data. It involves framing a null hypothesis versus an alternative hypothesis, calculating a test statistic, and comparing it to a critical value or p-value at a specified significance level to determine whether there is sufficient evidence to reject the null hypothesis.

Confidence Interval for Standard Deviation

Constructing a Confidence Interval for the Standard Deviation involves estimating the range within which the true population standard deviation is likely to fall, with a certain level of confidence (for example, 95%). This is typically achieved by using transformations that involve the chi-square distribution, which accounts for the sample variability in estimating the population variance or standard deviation.

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