An experiment is being conducted to compare the tension bond strength of polymer latex modified mortar to that of unmodified mortar. Let μ1 and μ2 be the true mean tension bond strengths for the modified and unmodified mortars respectively. The question of interest is whether the mean bond strength of modified mortars is larger than that of the unmodified mortars. Assume that the bond strength distributions are both normal. Assume that σ1 = 1.6 and σ2 = 1.4. Suppose the investigator decided to use a level 0.05 test and wished β = 0.10 to detect a difference of one unit between the two true means. If she decides to take a sample of size 35 of the modified mortars, what sample size does she need from the second population to accomplish what she wants? (Answer: 45)
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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