Suppose you take independent random samples from populations with means µg and µz and standard deviations o, and oz. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (ni and n2) are large. If X1 and X2 are the random sample means, then how does the quantity behave? Give the name of the distribution and any parameters needed to describe it.
Suppose you take independent random samples from populations with means µg and µz and standard deviations o, and oz. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (ni and n2) are large. If X1 and X2 are the random sample means, then how does the quantity behave? Give the name of the distribution and any parameters needed to describe it.
Suppose you take independent random samples from populations with means µg and µz and standard deviations o, and oz. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (ni and n2) are large. If X1 and X2 are the random sample means, then how does the quantity behave? Give the name of the distribution and any parameters needed to describe it.
Suppose you take independent random samples from populations with means μ1 and μ2 and standard deviations σ1 and σ2. Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n1 and n2) are large. If X1 and X2 are the random sample means, then how does the quantity
Give the name of the distribution and any parameters needed to describe it.
Transcribed Image Text:Suppose you take independent random samples from populations with
means µg and µ2 and standard deviations o, and oz. Furthermore, assume
either that (i) both populations have normal distributions, or (ii) the sample
sizes (na and n2) are large. If X1 and X2 are the random sample means, then
how does the quantity
behave? Give the
name of the distribution and any parameters needed to describe it.
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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