Is the Body Temperature of 98.6°F a Myth? 727 Explore the Data Here are important statistics from the sample of measured body temperatures. Note that the sample mean is 98.2°F, not 98.6°F. Any Outliers? Examination of the normal quantile plot and the minimum and maximum body temperatures reveals that there is one potential outlier: the minimum body temperature of 96.5°F. But when viewed as part of the lowest ten body temperatures (96.5, 96.9, 97.0, 97.0, 97.0, 97.1, 97.1, 97.1, 97.2, 97.3), the minimum of 96.5°F does not appear to be very far from the other lowest values, so that minimum value is not likely to have much of an impact on results. Apply Statistical Methods Hypothesis test using the parametric t test with a 0.05 significance level: Example 5 in Section 8-3 involved a hypothesis test of the common belief that the population mean is equal to 98.6°F. Results: With H0: m = 98.6°F and H1: m ≠ 98.6°F, the test statistic is t = -6.611, the P-value is 0.0000 (Table: P@value 60.005), the critical values are t = {1.983, so we reject H0 and conclude that there is sufficient evidence to warrant rejection of the common belief that the mean body temperature is equal to 98.6°F. (See the following Statdisk and Minitab displays for this hypothesis test.) Statdisk Results Minitab Results 95% confidence interval using the t distribution: Based on the preceding hypothesis test, we rejected the common belief that the mean body temperature is equal to 98.6°F, but that begs this question: If the mean body temperature is not 98.6°F, then what is it? A confidence interval gives us valuable information about that mean. The 95% confidence interval estimate of m is 98.08°F 6 m 6 98.32°F. We have 95% confidence that the mean body temperature is between 98.08°F and 98.32°F. Because the confidence interval does not include 98.6°F, we have strong evidence suggesting that the mean body temperature is not equal to 98.6°F. Randomization: Using the resampling method of randomization, shift the sample values so that the sample mean changes from 98.2°F to the claimed value of 98.6°F, and then use bootstrapping to generate 1000 samples. Using the sorted 1000 sample means, find the number of those sample means that are at least as extreme as 98.2°F. A typical randomization procedure will yield 1000 sample means such that the number of sample means that are at least as extreme as 98.2°F is 0 or close to 0. See the following displays from Statdisk and Minitab. (The Minitab P-value of less than continued
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