Smashing the Cooper Distance: Rescue Operation and Recovery Protocol
What is the 95% confidence interval for the population mean distance male firefighters can run in a Cooper test after the recovery protocol?
The 95% confidence interval for the population mean distance male firefighters can run in a Cooper test after the recovery protocol is approximately 2.419 km to 2.715 km.
Calculation Process
Given that the sample mean is 2.567 km, the standard deviation is 0.358 km, and the sample size is 25, we need to determine the critical value and the standard error. The critical value for a 95% confidence interval can be found using a t-distribution table or a statistical calculator. For a sample size of 25, the critical value is approximately 2.064. The standard error is calculated by dividing the standard deviation by the square root of the sample size:
standard error = 0.358 km / √25 = 0.0716 km. Substituting the values into the formula, we get:
CI = 2.567 km ± (2.064 * 0.0716 km). Simplifying the expression, we have:
CI = 2.567 km ± 0.148 km. Therefore, the 95% confidence interval for the population mean distance male firefighters can run in a Cooper test after the recovery protocol is approximately 2.419 km to 2.715 km.