Suppose the yield (lb/acre) of corn from 2 types of soil is studied for years and the means and variances are known to be mean variance Type A 4500 455,625 Type B 3900 152,100 a) What is the mean and variance of the differences between the sample means from the two types of soil with 10 and 15 observations, respectively? What is the standard error of the differences? (600; 55,702.5; 236.01) b) Calculate the mean and standard error of the difference assuming the above sample sizes were 40 and 60, respectively. (600, 118.01)

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Description: Suppose the yield (lb/acre) of corn from 2 types of soil is studied for years and the means and variances are known to be mean variance Type A 4500 455,625 Type B 3900 152,100 a) What is the mean and variance of the differences between the sample mea

Type A Type B Mean 4500 3900 Variance 455,625 152,100 , For part a) n1 = 10 and n2 =…

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Suppose the yield (lb/acre) of corn from 2 types of soil is studied for years and the means

and variances are known to be

mean variance Type A 4500 455,625 Type B 3900 152,100

a) What is the mean and variance of the differences between the sample means from the

two types of soil with 10 and 15 observations, respectively? What is the standard error of the differences? (600; 55,702.5; 236.01)

b) Calculate the mean and standard error of the difference assuming the above sample sizes

were 40 and 60, respectively. (600, 118.01)

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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