Suppose a hypertension trial is mounted and 18 participants are randomly assigned to one of the comparison treatments. Each participant takes the assigned mediaction and his or her systolic blood pressure is recorded after 6 months on the assigned treatment. The data are as follows:       Standard treatment           Placebo                    New Treatment            124                                    134                          114           111                                     143                          117            133                                      148                         121            125                                      142                         124             128                                      150                         122               115                                    160                         128  Is there a difference in Mean systolic blood pressure among treatments? Run the appropriate test at a=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 + ...