Relationship Between Sample Data and Population Values

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Relationship Between Sample Data and Population Values

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Relationship Between Sample Data and Population Values.

Relationship Between Sample Data and Population Values

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Relationship Between Sample Data and Population Values

You will encounter many situations in business where a sample will be taken from a population, and you will be required to analyze the sample data. Regardless of how careful you are in using proper sampling methods, the sample likely will not be a perfect reflection of the population.

A Sampling Distribution is the probability distribution for a statistic. Its description includes:

- all possible values that can occur for the statistic; and
- the probability of each value or each interval of values for a given sample.

- Population Mean (µX):
µX = 170,000 / 5 = $34,000

- Population Standard Deviation (X):
X = [SQRT(898*106) / 5] = $13,401.49

- How many random samples of three can you draw from this population?
5C3 = 10 samples of three can be drawn form this population. Each sample has a 1 / 5C3 , or 1 / 10 chance of being selected.

- List the sample space and find sample means.

- The mean of the samples means:
µX = ( X1 + X2 + …. + Xn ) / NCn

µX = 340,000 / 10 = $34,000

- The Standard Deviation the samples means, better known as the Standard Error of the Mean:
X = SQRT[( Xi - µX )2 / NCn]

- The standard error of the mean indicates the spread in the distribution of all possible sample means.
- Xis also equal to the population standard deviation divided by the SQRT of the sample size
X = X / SQRT(n)

- For n > 0.05N, the finite population correction factor adjusts the standard error to most accurately describe the amount of variation.
- The fpc is SQRT[( N - n ) / ( N - 1 )]