Answered: Distribution A is a distribution of…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.4: Expected Value

Problem 20E

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Distribution A is a distribution of sample means with a mean of 50 and standard error of 5. Distribution B is also a distribution of sample means with a mean of 50, however the standard error is 30. If you drew 2 random samples each from A and B, for which would you expect the samples to be more similar to each other?

a, Samples from either distribution would be equally reliable.

b. samples from Distribution A would be more similar to each other than samples from distribution B

c. There is no way to determine how similar or reliable we should expect the samples to be.

d. samples from Distribution B would be more similar to each other than samples from distribution A

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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