# Relationship Between Sample Data and Population Values - PowerPoint PPT Presentation

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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

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.

### Sampling Distribution

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 Parameters

• Population Mean (µX):

µX = 170,000 / 5 = \$34,000

• Population Standard Deviation (X):

X = [SQRT(898*106) / 5] = \$13,401.49

### Draw a Random Sample of Three

• 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 Sampling Distribution of Sample Means ( X )

• 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]

### Standard Error of the Mean

• 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)

### A Finite Population Correction Factor (fpc)

• 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 )]