Answer :
The 95% confidence interval (98.1, 98.4) for the mean body temperature indicates that we are 95% confident that the population mean body temperature falls between 98.1 ºF and 98.4 ºF. (option a).
This confidence interval does not refer to individual body temperatures within a sample or the body temperatures of specific individuals. Instead, it provides a range within which we estimate the true population mean body temperature to lie with 95% confidence.
To explain further, a confidence interval is a statistical range that likely contains the true parameter value—in this case, the mean body temperature of all healthy adults.
The interval (98.1, 98.4) tells us that if we were to repeatedly sample healthy adults and compute the mean body temperature from each sample, we would expect the true population mean (the actual average body temperature of all healthy adults) to fall within this interval in approximately 95% of such samples.
The margin of error (m) for this interval is half the width of the interval.
Therefore, [tex]\( m = \frac{98.4 - 98.1}{2} = 0.15 \)[/tex] ºF. This means the true mean body temperature of the population is estimated to be between [tex]\(98.1 - 0.15\)[/tex] ºF and [tex]\(98.4 + 0.15\)[/tex] ºF, or between 98.25 ºF and 98.55 ºF, with 95% confidence.
Therefore, the correct interpretation of the interval is that we are 95% confident that the true mean body temperature of the entire population of healthy adults falls between 98.1 ºF and 98.4 ºF.
The margin of error, calculated as half the width of the interval, is 0.15 ºF. (option a).
