Final answer:
The 99% confidence interval for the mean pulse rate of all U.S. adult males who jog at least 15 miles per week can be calculated using the sample mean and standard deviation, along with the t-distribution for a 99% confidence level and n-1 degrees of freedom.
Step-by-step explanation:
To find the 99% confidence interval for the mean pulse rate of all U.S. adult males who jog at least 15 miles per week, given the sample pulse rates, we first compute the sample mean (μ) and the sample standard deviation (s). Using the given data points, the sample mean is (54 + 50.5 + 50.8 + 53 + 52.5 + 53 + 54 + 52 + 53.5 + 55) / 10 = 52.83 beats per minute. The sample standard deviation can be calculated using the formula for s in a normal distribution. Once these statistics are calculated, the confidence interval can be found using the formula for a t-interval, since the population standard deviation is unknown and the sample size is small (n < 30).
We use a t-distribution with n-1 degrees of freedom (where n is the sample size). The t-score corresponding to a 99% confidence level can be found using a t-distribution table or statistical software. The confidence interval is then given by:
μ ± (t* × (s/√n))
where μ is the sample mean, t* is the t-score for 99% confidence and n-1 degrees of freedom, s is the sample standard deviation, and n is the sample size. This calculation will provide the lower and upper bounds of the 99% confidence interval for the mean pulse rate.