1 / 69

Chapter 17 Determinants of Sample Size

Chapter 17 Determinants of Sample Size. Basic Terminology. Statistics is the science that deals with the collecting, analyzing and interpreting data. Descriptive Statistics describe the characteristics of a population.

stephanie-hebert
Download Presentation

Chapter 17 Determinants of Sample Size

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 17 Determinants of Sample Size

  2. Basic Terminology • Statistics is the science that deals with the collecting, analyzing and interpreting data. • Descriptive Statistics describe the characteristics of a population. • Inferential Statistics is used to make an inference about a population from a sample.

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

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

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

  6. 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

  7. 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

  8. 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

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

  10. Population Mean

  11. Sample Mean

  12. 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

  13. 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

  14. Measures of Dispersion • The range • Standard deviation

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

  16. 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

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

  18. Low Dispersion Verses High Dispersion Low Dispersion Frequency 150 160 170 180 190 200 210

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

  20. AverageDeviation

  21. Mean Squared Deviation

  22. The Variance

  23. Variance

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

  25. Sample Standard Deviation

  26. Population Standard Deviation

  27. Sample Standard Deviation

  28. Sample Standard Deviation

  29. 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

  30. Normal Distribution MEAN

  31. Normal Distribution 13.59% 13.59% 34.13% 34.13% 2.14% 2.14%

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

  33. Standardized Normal Distribution • Symmetrical 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

  34. 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

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

  36. Standardized Scores

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

  38. 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

  39. Population distribution • Sample distribution • Sampling distribution

  40. Population Distribution m -s s x

  41. Sample Distribution _ C X S

  42. Sampling Distribution

  43. Definitions • A frequency distribution of the population is called a population distribution. • A frequency distribution of a sample is called a sample distribution. • The sampling distribution is a theoretical probability distribution that in actual practice would never be calculated. • It is a theoretical probability distribution that shows the functional relationship between the possible values of some summary characteristic of n cases drawn at random and the probability associated with each value over all possible samples of size n from a particular population.

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

  45. Central Limit Theorem • As sample size increases, the distribution of the mean of random samples, taken from practically any population, approaches a normal distribution. • The central limit theorem works regardless of the shape of the original population distribution.

  46. Standard Error of the Mean

  47. Parameter Estimates • Point estimates • Confidence interval estimates

  48. Confidence Interval

More Related