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

2. Population Parameter Versus Sample Statistics

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 (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 Frequency Distribution of Deposits

7. 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 Percentage Distribution of Amounts of Deposits

8. 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 Probability Distribution of Amounts of Deposits

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

13. Product AProduct B 196150 198160 199176 199181 200192200 200201 201202 201213 201224 202240 202261 Sales for Products A and B, Both Average 200

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

15. 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

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

17. 150 160 170 180 190 200210 5432154321 Low Dispersion Value on Variable Frequency Low Dispersion Verses High Dispersion

18. 150 160 170 180 190 200210 5432154321 Frequency High dispersion Value on Variable Low Dispersion Verses High Dispersion

19. Average Deviation

20. Mean Squared Deviation

21. The Variance

22. Variance

23. The variance is given in squared units The standard deviation is the square root of variance:

24. Sample Standard Deviation

25. Population Standard Deviation

26. Sample Standard Deviation

27. 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

28. MEAN Normal Distribution

29. 2.14% 13.59% 34.13% 13.59% 2.14% Normal Distribution

30. 85115 100 14570 Normal Curve: IQ Example

31. 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

32. Standard Normal Curve Mean of zero, standard deviation of 1 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

33. 0 1 -2 2 z A Standardized Normal Curve

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

35. Standardized Scores

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

37. Linear Transformation of Any Normal Variable Into a Standardized Normal Variable -2 -1 0 1 2 Sometimes the scale is stretched Sometimes the scale is shrunk    X

38. Population distribution Sample distribution Sampling distribution

39.  x  Population Distribution

40.  X S Sample Distribution

41. Sampling Distribution

42. Standard Error of the Mean Standard deviation of the sampling distribution

43. Central Limit Theorem The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

44. Standard Error of the Mean

46. Estimation of Parameter Point estimates Confidence interval estimates

47. Confidence Interval

51. Estimating the Standard Error of the Mean

53. Random Sampling Error and Sample Size are Related

54. Sample Size Variance (standard deviation) Magnitude of error Confidence level

55. Sample Size Formula

56. Sample Size Formula - Example Suppose a survey researcher, studying expenditures on lipstick, wishes to have a 95 percent confident level (Z) and a range of error (E) of less than $2.00. The estimate of the standard deviation is $29.00.

57. Sample Size Formula - Example

58. Suppose, in the same example as the one before, the range of error (E) is acceptable at $4.00, sample size is reduced. Sample Size Formula - Example

60. 99% Confidence Calculating Sample Size  1389  265.37 2  2 53.74 2        2 )29)(57.2( n 2         347   6325.18 2  4 53.74 2        4 )29)(57.2( n 2       

61. Standard Error of the Proportion

62. Confidence Interval for a Proportion

63. Sample Size for a Proportion

64. 2 2 E pqz n  Where: n = Number of items in samples Z 2 = The square of the confidence interval in standard error units. p = Estimated proportion of success q = (1-p) or estimated the proportion of failures E 2 = The square of the maximum allowance for error between the true proportion and sample proportion or zs p squared.

65. Calculating Sample Size at the 95% Confidence Level 753  001225. 922.  001225 )24)(.8416.3(  )035(. )4 )(. 6(.) 96 1. ( n 4.q 6.p 2 2   