Study Details for Problems 1 4: An exercise science researcher conducted a study on resting heart rates of athletes. They collected data from a random sample of 36 collegiate athletes, and found that their average resting heart rate was 58.3 beats per minute (bpm) with a sample standard deviation of 5.2 bpm. They used this data to construct a 95% confidence interval for the true mean resting heart rate of all collegiate athletes. The DCMP Data Analysis Tool output is provided below. The general formula for a confidence interval is also provided. Screen Shot 2025-08-12 at 8.03.24 AM.png The DCMP Data Analysis Tool output shows that the standard error of the mean is 0.8667. What does this value represent in this situation? With 95% confidence, individual athletes' heart rates vary by about 0.8667 bpm. 86.67% of the sample means will fall within 0.8667 bpm of the population mean. The standard deviation of sample means we would obtain from repeated samples of size 36 is about 0.8667 bpm. 86.67% of the sample means will fall within 0.8667 bpm of the population mean. In a 95% confidence interval, the sample mean is expected to be within 0.8667 bpm of the true mean.

Estimate of Population Mean: t- Margin S Point Standard score of Estimate Error (df=35) Error 58.3 0.8667 2.0301 1.759 Confidence Interval: Population Parameter Lower Bound Upper Bound Confidence Level Mean 56.54 60.06 95% 95% Confidence Interval [56.54, 60.06] 54 56 58 60 62 X Population Mean