The mean length of time required to perform a certain assembly line task at Joe's Manufacturing has been established to be 15.5 minutes, with a standard deviation of 3 minutes. A random sample of 9 employees is taught a new method. After a training period, the average time these 9 employees take to preform the same task is 13.5 minutes. The plant manager would like to be at least 97.5% sure before switching any more employees to the new, perhaps faster method and consults you for advice. Do these results provide sufficient evidence to indicate that he new method is faster than the old? Use the critical value approach to develop and test the appropriate hupotheses concerning this situation. What would you advise the manager under these circumstances?
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 + ...
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