Question

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Researchers have questioned whether the traditional value of 98.6°F is correct for a typical body temperature for healthy adults. Suppose that you plan to estimate mean body temperature by recording the temperatures of the people in a random sample of 10 healthy adults and calculating the sample mean. How accurate can you expect that estimate to be? In this activity, you will develop a margin of error that will help you to answer this question.


Let's assume for now that body temperature for healthy adults follows a normal distribution with mean 98.6 degrees and standard deviation 0.7 degrees. Here are the body temperatures for one random sample of 10 healthy adults from this population:

1. What is the mean temperature for this sample?



2. If you were to take a different random sample of size 10, would you expect to get the same value for the sample mean? Explain.

Answer 1

1. The mean temperature for this sample can be found by adding up the temperatures and dividing by the sample size of 10:

98.6 + 98.5 + 98.8 + 98.2 + 98.1 + 99.0 + 98.3 + 98.5 + 98.9 + 98.7 = 986.6

986.6 / 10 = 98.66

Therefore, the mean temperature for this sample is 98.66 degrees.

2. No, we would not expect to get the exact same value for the sample if we were to take a different random sample of size 10. This is because random sampling means that each sample will be slightly different from each other, and the sample mean will vary based on the particular individuals included in each sample. However, we would expect the sample means to be similar and clustered around the true population mean of 98.6 degrees. The variability of the sample means can be quantified using the standard error of the mean, which is a measure of the average distance that the sample means are from the true population mean. The standard error of the mean decreases as the sample size increases, meaning that larger samples are more likely to provide a more accurate estimate of the population mean.

Explanation: