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Answer :
The 99% confidence interval estimate of the mean body temperature of all healthy humans is 98.124°F < μ < 98.276°F. The sample suggests that the commonly accepted value of 98.6°F as the mean body temperature may not be accurate.
To construct a confidence interval estimate of the population mean μ, we can use the formula: x-hat ± t * (s / √n), where x-hat is the sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value from the t-distribution corresponding to the desired level of confidence.
Given the sample information, x-hat = 98.2°F, s = 0.65°F, and n = 108, we need to determine the critical value of t for a 99% confidence level. With a sample size of 108 and degrees of freedom (df) equal to n - 1 = 107, the critical value can be obtained from the t-table or using statistical software.
Looking up the critical value for a 99% confidence level with 107 degrees of freedom, we find it to be approximately 2.617.
Substituting the values into the confidence interval formula, we have: 98.2°F ± 2.617 * (0.65°F / √108).
Calculating the interval, we find: 98.124°F < μ < 98.276°F.
Therefore, the 99% confidence interval estimate for the population mean body temperature μ is 98.124°F < μ < 98.276°F. This suggests that the commonly accepted value of 98.6°F may not be accurate, as it falls outside the confidence interval.
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