Question

Clinical literature reports that the duration of a typical cold is roughly 18 days. Researchers wanted to know if people tend to underestimate the duration of a typical cold, on average. They surveyed a random sample of 352 healthy adults in Georgia and asked them how long they think that a typical cold lasts. The researchers reported a 95% confidence interval of 6.9 to 8.2 days for the mean expected duration of typical cold.

Which of the following is the correct interpretation for this confidence interval?
a. We are 95% confident that the sample mean duration is between 6.9 and 8.2 days.
b. We are 95% confident that the population mean duration is between 6.9 and 8.2 days.
c.There is a 95% chance that the mean duration of another random sample from this population would be between 6.9 and 8.2 days.
d. There is a 95% chance that a randomly selected individual from this population would give a response between 6.9 and 8.2 days.

Answer 1

b. We are 95% confident that the population mean duration is between 6.9 and 8.2 days.

Explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

95% confidence interval of 6.9 to 8.2 days for the mean expected duration of typical cold.

This means that we are 95% sure that the true duration of a typical cold(population mean) for all health adults in Georgia is between 6.9 and 8.2, which means that the correct answer is given by option b.