(5 points)

Smashing the Cooper distance ~ Rescue operations conducted by firefighters involve intense physical activity associated with high levels of cardiovascular stress. In 2020, a group of French researchers investigated the claim that a combination of deep breathing and mental imagery promotes cardiovascular recovery in firefighters. The researchers recruited a random sample of 24 male professional firefighters for their study.To get a baseline measurement, the researchers subjected the firefighters to the Cooper test, a popular maximal test of aerobic fitness during which a participant runs as far as possible in 12 minutes. The mean distance among the 24 participants in the baseline measurements was 2.699 km with a standard deviation of 0.355 km.Round all calculated values to 4 decimal places as appropriate.1. Consider the 24 firefighters as a random sample of all male firefighters. Calculate a 99% confidence interval for the population mean distance male firefighters can run in a baseline Cooper test.( , )

2. If the researchers wanted to estimate the population mean distance male firefighters can run in a baseline Cooper test with 99% confidence and a margin of error of no more than 0.09 km, how large a sample size would they need?Use a tt value rounded to three decimal places and the sample information above to calculate your answer. Your answer should be an integer value.n=n=

After the baseline Cooper test, the researchers led the firefighters in a recovery protocol of 30 minutes of deep breathing and mental imagery. The firefighters then completed a second Cooper test. Researchers used the post-recovery test results and calculated a 95% confidence interval for the population mean distance male firefighters can run in a Cooper test after the recovery protocol as (0.85, 1.15) km.3. Assuming the researchers performed the calculations correctly, identify whether each statement below is an appropriate or inappropriate interpretation of the confidence interval. ? appropriate inappropriate We can be 95% confident that the true mean distance male firefighters can run in a Cooper test after the recovery protocol is between 0.85 and 1.15 km. ? appropriate inappropriate Approximately 95% of male firefighers will be able to run between 0.85 and 1.15 km in a Cooper test after the recovery protocol.