A group of Americans participated in a study that involved taking their temperatures during exercise in extreme heat. The participants had a mean body temperature of 104°F and a standard deviation of 2°F. Doctors analyzing the results prefer to work in degrees Celsius, so they convert the data by applying the formula below to each data point: °C = 5/9(°F - 32) If each temperature is converted to degrees Celsius, what will be the mean and standard deviation of the distribution of new temperatures? Choose 1 answer: A Mean: 57.8°C Standard deviation: 2°C B Mean: 57.8°C Standard deviation: 1.11°C C Mean: 40°C Standard deviation: 2°C D Mean: 40°C Standard deviation: 1.11°C
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Step 1: First, we need to convert the mean body temperature from Fahrenheit to Celsius using the given formula: \[ \text{°C} = \frac{5}{9} (\text{°F} - 32) \] Show more…
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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.
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