Relationship Between Sample Data and Population Values You will encounter many situations in business where a sample will be taken from a population, and.

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Presentation transcript:

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.

Example

Population Parameters Population Mean (µ X ): µ X = 170,000 / 5 = $34,000 Population Standard Deviation (  X ):  X = [SQRT(898*10 6 ) / 5] = $13,401.49

Draw a Random Sample of Three How many random samples of three can you draw from this population? 5 C 3 = 10 samples of three can be drawn form this population. Each sample has a 1 / 5 C 3, or 1 / 10 chance of being selected. List the sample space and find sample means.

Ten Possible Samples

The Sampling Distribution of Sample Means ( X ) The mean of the samples means: µ X = ( X 1 + X 2 + …. + X n ) / N C n µ X = 340,000 / 10 = $34,000 The Standard Deviation the samples means, better known as the Standard Error of the Mean:  X = SQRT[( X i - µ X ) 2 / N C n ]

Standard Error of the Mean The standard error of the mean indicates the spread in the distribution of all possible sample means.  X is 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 )]