. On the basis of her newly developed technique, a student believes she can reduce the amount of time schizophrenics spend in an institution.  As director of training at a nearby institution, you agree to let her try her method on 20 schizophrenics, randomly sampled from your institution.  The mean duration that schizophrenics stay at your institution is 85 weeks, with a standard deviation of 15 weeks.  The scores are normally distributed.  The results of the experiment show that patients treated by the student stay at the institution a mean duration of 78 weeks.  What do you conclude about the student’s technique?  Use α = .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 + ...