Researchers constructed a confidence interval for the mean body temperature of healthy US adults, using a random sample of 1000 healthy adults in the US. They found their 99% confidence interval to be (97, 99) degrees Fahrenheit. Which of the following statements are correct? Select one or more:
a. A 90% confidence interval calculated using the same sample data would be narrower than the given confidence interval.

b. If we were to repeatedly take random samples of 1000 healthy US adults and construct 99% confidence intervals with each sample, approximately 99% of these confidence intervals will contain the true average body temperature of all healthy US adults.

c. We are 99% confident that the average body temperature of the 1000 adults in any randomly selected sample will be between 97 and 99 degrees Fahrenheit.
d. The sample mean body temperature of the 1000 adults in our specific sample y¯
y
¯
is between 97 and 99.

e. If we were to select a new sample of 2000 adults and created a new confidence interval, the width of the new confidence interval would increase.

f. We are 99% confident that the average body temperature of all healthy US adults is between 97 and 99 degrees Fahrenheit.