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Business Research Methods William G. Zikmund

Business Research Methods William G. Zikmund. Chapter 17: Determination of Sample Size . What does Statistics Mean?. Descriptive statistics Number of people Trends in employment Data Inferential statistics Make an inference about a population from a sample.

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Business Research Methods William G. Zikmund

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  1. BusinessResearch MethodsWilliam G. Zikmund Chapter 17: Determination of Sample Size

  2. What does Statistics Mean? • Descriptive statistics • Number of people • Trends in employment • Data • Inferential statistics • Make an inference about a population from a sample

  3. Population Parameter Versus Sample Statistics

  4. Population Parameter • Variables in a population • Measured characteristics of a population • Greek lower-case letters as notation

  5. Sample Statistics • Variables in a sample • Measures computed from data • English letters for notation

  6. Making Data Usable • Frequency distributions • Proportions • Central tendency • Mean • Median • Mode • Measures of dispersion

  7. Frequency Distribution of Deposits Frequency (number of people making deposits Amount in each range) less than $3,000 499 $3,000 - $4,999 530 $5,000 - $9,999 562 $10,000 - $14,999 718 $15,000 or more 811 3,120

  8. Percentage Distribution of Amounts of Deposits Amount Percent less than $3,000 16 $3,000 - $4,999 17 $5,000 - $9,999 18 $10,000 - $14,999 23 $15,000 or more 26 100

  9. Probability Distribution of Amounts of Deposits Amount Probability less than $3,000 .16 $3,000 - $4,999 .17 $5,000 - $9,999 .18 $10,000 - $14,999 .23 $15,000 or more .26 1.00

  10. Measures of Central Tendency • Mean - arithmetic average • µ, Population; , sample • Median - midpoint of the distribution • Mode - the value that occurs most often

  11. Population Mean

  12. Sample Mean

  13. Number of Sales Calls Per Day by Salespersons Number of Salesperson Sales calls Mike 4 Patty 3 Billie 2 Bob 5 John 3 Frank 3 Chuck 1 Samantha 5 26

  14. Sales for Products A and B, Both Average 200 Product A Product B 196 150 198 160 199 176 199 181 200 192 200 200 200 201 201 202 201 213 201 224 202 240 202 261

  15. Measures of Dispersion • The range • Standard deviation

  16. Measures of Dispersion or Spread • Range • Mean absolute deviation • Variance • Standard deviation

  17. The Range as a Measure of Spread • The range is the distance between the smallest and the largest value in the set. • Range = largest value – smallest value

  18. Deviation Scores • The differences between each observation value and the mean:

  19. Low Dispersion Verses High Dispersion 5 4 3 2 1 Low Dispersion Frequency 150 160 170 180 190 200 210 Value on Variable

  20. Low Dispersion Verses High Dispersion 5 4 3 2 1 High dispersion Frequency 150 160 170 180 190 200 210 Value on Variable

  21. AverageDeviation

  22. Mean Squared Deviation

  23. The Variance

  24. Variance

  25. Variance • The variance is given in squared units • The standard deviation is the square root of variance:

  26. Sample Standard Deviation

  27. Population Standard Deviation

  28. Sample Standard Deviation

  29. Sample Standard Deviation

  30. The Normal Distribution • Normal curve • Bell shaped • Almost all of its values are within plus or minus 3 standard deviations • I.Q. is an example

  31. Normal Distribution MEAN

  32. Normal Distribution 13.59% 13.59% 34.13% 34.13% 2.14% 2.14%

  33. Normal Curve: IQ Example 70 145 85 115 100

  34. Standardized Normal Distribution • Symetrical about its mean • Mean identifies highest point • Infinite number of cases - a continuous distribution • Area under curve has a probability density = 1.0 • Mean of zero, standard deviation of 1

  35. Standard Normal Curve • The curve is bell-shaped or symmetrical • About 68% of the observations will fall within 1 standard deviation of the mean • About 95% of the observations will fall within approximately 2 (1.96) standard deviations of the mean • Almost all of the observations will fall within 3 standard deviations of the mean

  36. A Standardized Normal Curve z 1 2 -2 -1 0

  37. The Standardized Normal is the Distribution of Z –z +z

  38. Standardized Scores

  39. Standardized Values • Used to compare an individual value to the population mean in units of the standard deviation

  40. Linear Transformation of Any Normal Variable Into a Standardized Normal Variable s s m X m Sometimes the scale is stretched Sometimes the scale is shrunk -2 -1 0 1 2

  41. Population distribution • Sample distribution • Sampling distribution

  42. Population Distribution m -s s x

  43. Sample Distribution _ C X S

  44. Sampling Distribution

  45. Standard Error of the Mean • Standard deviation of the sampling distribution

  46. Central Limit Theorem

  47. Standard Error of the Mean

  48. Parameter Estimates • Point estimates • Confidence interval estimates

  49. Confidence Interval

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