Participants were enrolled in a health-coaching program for eight weeks to try to improve physical health and overall wellness. At the end of the trial period, the participants take a personal health improvement survey. The mean health improvement survey score for all participants in the program was 74.4 with a standard deviation of 10.3. We have reason to think that one of the health coaches (Coach A) who participated in an additional training program will have subjects who have higher health improvement survey scores than the overall program average. We know that Coach A trains 30 subjects with the average health improvement survey score of 80.1. a) We want to test the hypothesis that subjects who work with Coach A have higher health improvement survey scores compared with the rest of the program participants. Use alpha of 0.05

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 + ...