For a healthy adult, body temperature follows a normal distribution with a mean of 98.2 degrees and a standard deviation of 0.73. We take a random sample of 30 people who have strep throat and are tested with this rapid strep test. Let x be the number of people who receive false negatives. Since we will not be sampling with replacement, assume that we are sampling from a population that is large enough so that the probability of success is close enough to the same in each trial that the sampling can be considered independent.

Is the statement above true or false?

a) True
b) False

The statement that sampling can be considered independent in a study of body temperatures in a large population is true, because the small sample size doesn't significantly affect the probability of success in each trial.

Explanation:

The question addresses the concepts of normal distribution, standard deviation, statistical significance, and hypothesis testing in the context of health, specifically relating to body temperature. For a healthy adult, the question states that body temperature follows a normal distribution with a mean of 98.2 degrees Fahrenheit and a standard deviation of 0.73 degrees. Given a random sample of 30 people with strep throat, we are to determine if we can consider the probability of success as constant enough to assume that the sampling can be considered independent, even without replacement. This is a principle used in statistics when the population is large enough to not affect the probability of an outcome with each trial.

In this case, the statement can be considered true because the sample size is relatively small compared to the population and thus the probability of success is not significantly altered by the removal of an individual from the population. Hence, we can use inferential statistics like the z-test or t-test to make statements about the population's mean body temperature based on the sample. For example, if we had to test if the mean body temperature of the sample is significantly different than the mean body temperature of the general population, and the population variance is unknown, we would use the t-distribution.