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CHAPTER 13

CHAPTER 13. DETERMINING THE SIZE OF A SAMPLE. Important Topics of This Chapter. Different Methods of Determining Sample size. Standard Normal Distribution and the Nation of Confidence Interval. The Notion of Sampling Distribution and Standard Error of a Mean.

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CHAPTER 13

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  1. CHAPTER 13 DETERMINING THE SIZE OF A SAMPLE

  2. Important Topics of This Chapter • Different Methods of Determining Sample size. • Standard Normal Distribution and the Nation of Confidence Interval. • The Notion of Sampling Distribution and Standard Error of a Mean. • Computing Sample Size Using a Mean.

  3. Sample Size Determination • Arbitrary Approach: • Rule of thumb. • Conventional Approach: • Average of similar studies. • Cost Basis Approach: • Availability of resources. • Statistical Analysis Approach: • Statistical considerations. • Confidence Interval Approach: • Concept of variability, sampling distribution and standard error of the mean.

  4. THE STANDART NORMAL DISTRIBUTION • It is a bell shaped curve and the mean is at the center. • It is defined with its mean and standard deviation • Total area under the curve is equal to 1.0., or 100%. • One standard deviation under the curve is equal to 34% to the right and 34% to the left. Therefore, total area of one standard deviation to the left and to the right of the mean is equal to 68.26%. Therefore, the total area of two standard deviation to the left and the right under the curve is equal to 95 percent and the total area of three standard deviation to the left and to right under the curve is 99 percent. • Accordingly, the mean of Standard Normal Distribution is equal to zero (Z=0).

  5. Z=0 Standard Normal Distribution 0.50 0.50

  6. _ Z=-1 X Z=1 68% Confidence Interval 0.34 0.34

  7. _ Z=-2 X Z=2 95% Confidence Interval 0.475 0.475

  8. _ Z= -3 X Z=3 99% Confidence Interval 0.495 0.495

  9. SAMPLE AND SAMPLING DISTRIBUTION • Sample Distribution: Frequency distribution of the (single)sample represented by sample mean(x) and sample standard deviation(s). • Central Limit Theorem: Increasing sample size regardless of the shape of distribution resulting to reach to normal distribution. • Standard error of the mean: • It is equal to population standard deviation divided by the square root of the sample size. If you cannot find the population standard deviation, you can use sample standard deviation. Its formula is: s Sx=--------- n • If the the standard error of the mean is zero, it means that sample mean is equal to population mean.

  10. Finding Probabilities Corresponding to Known Values Area is 0.3413 Z Scale

  11. Finding Values Corresponding to Known Probabilities Area is 0.500 Area is 0.450 Area is 0.050 X Scale X 50 Z Scale -Z 0

  12. Area is 0.025 Finding Values Corresponding to Known Probabilities: Confidence Interval Area is 0.475 Area is 0.475 Area is 0.025 X Scale X 50 Z Scale -Z -Z 0

  13. Sample Size Determination Using Mean • The formula is: s2z2 n = --------- Where: e2 n=sample size z=the level confidence associated with standard error. s=variability indicated by an estimated standard deviation. e=the amount of precision or allowable error.

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