Sample Size. In Exercises 29–36, find the sample size required to estimate the population mean. Mean Weight of Male Statistics Students Data Set 1 “Body Data” in Appendix B includes weights of 153 randomly selected adult males, and those weights have a standard deviation of 17.65 kg. Because it is reasonable to assume that weights of male statistics students have less variation than weights of the population of adult males, let σ = 17.65 kg. How many male statistics students must be weighed in order to estimate the mean weight of all male statistics students? Assume that we want 90% confidence that the sample mean is within 1.5 kg of the population mean. Does it seem reasonable to assume that weights of male statistics students have less variation than weights of the population of adult males?
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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