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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

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  1. 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.

  2. 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.

  3. Example

  4. Population Parameters • Population Mean (µX): µX = 170,000 / 5 = $34,000 • Population Standard Deviation (X): X = [SQRT(898*106) / 5] = $13,401.49

  5. 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.

  6. Ten Possible Samples

  7. 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]

  8. 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)

  9. 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 )]

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