experiment, some subjects from each group had dropped out and the following data were obtained: Control Group Experimental Group nc = 38 nE = 34 X-barc = 75 Sc= 14.5 SE X-barE = 80 = 16.2 a) Test the research hypothesis that the sample means are significantly different from one another (a ≤.05). b) If X-barc is still equal to 75, and both groups' sample sizes and standard deviations remain unchanged, at least how high would X-bare have to be to be considered significantly higher than X-barc (a ≤.05)? c) Suppose both groups' means and standard deviations are unchanged but nc is now 12 and nE is 8. Is X-barE significantly higher than X-barc (a ≤.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 + ...