As part of an overall evaluation of training methods, an experiment was conducted to determine the average exercise capacity of healthy male army inductees. To do this, each male in a random sample of 35 healthy army inductees exercised on a bicycle ergometer (a device for measuring work done by the muscles) under a fixed workload until he tired. Blood pressure, pulse rates, and other indicators were carefully monitored to ensure that no one’s health was in danger. The exercise capacities (mean time, in minutes) for the 35 inductees are listed in the data 1. Use these data to construct a 95% confidence interval for m, the average exercise capacity for healthy male inductees. Interpret your findings. Using the data, to determine the number of sample observations that would be required to estimate m to within 1 minute, using a 95% confidence interval. 2. Are you using a Z or a t interval? why? 3. What assumptions do you need to meet? Use the following data: 'capacity' 23 28 35 42 21 19 14 25 45 49 36 44 29 23 27 12 15 17 29 39 41 46 51 18 44 43 36 33 14 18 19 25 47 48 13

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...