College

A 95% confidence interval for the true mean cholesterol of adult males, based on 25 randomly selected subjects, extends from 175 mg/L to 250 mg/L. A proper interpretation of the confidence interval would be that:

a. In repeated samples of size 25, the sample mean will fall between 175 and 250 mg/L 95% of the time.

b. There is a 95% chance that a randomly selected individual has a cholesterol level that falls between 175 and 250 mg/L.

c. Exactly two of the interpretations are correct.

d. 95% of the population has a cholesterol level between 175 and 250 mg/L.

e. We are 95% confident that the true mean cholesterol level of the population falls between 175 and 250 mg/L.

f. None of the interpretations are correct.

Answer :

The correct interpretation of the 95% confidence interval in this context is that we're 95% confident that the true mean cholesterol level of the population falls between 175 and 250 mg/L. This statement is about the mean of the population, not individual observations or repeated samples.

The correct interpretation of the confidence interval given is: we are 95% confident that the true mean cholesterol level of the population falls between 175 and 250 mg/L. This means, if we would to sample the population infinitely many times and calculate the 95% confidence interval for each sample, about 95% of these intervals would contain the true population mean. This does not mean that 95% of individuals have a cholesterol level between these values, or that there is a 95% chance that any individual selected will have a cholesterol level within this range. It's a statement about the mean of the population not about individual observations or repeated samples. So the answer is e.

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