1. Business Research Methods William 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
DepositsAmountPercentless 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 DepositsAmount
Probabilityless than $3,000 .16$3,000 - $4,999 .17$5,000 - $9,999
.18$10,000 - $14,999 .23$15,000 or more .26
10. Measures of Central Tendency Mean - arithmetic average ,
Population; X , sample Median - midpoint of the distribution Mode -
the value that occurs most often
11. Population Mean X = i N
12. Sample Mean XiX= n
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 200Product A
Product B 196 150 198 160 199 176 199 181 200 192 200 200 200
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: d x x i = i
19. Low Dispersion Verses High Dispersion 5 Low
DispersionFrequency 4 3 2 1 150 160 170 180 190 200 210 Value on
Variable
20. Low Dispersion Verses High Dispersion 5Frequency 4 High
dispersion 3 2 1 150 160 170 180 190 200 210 Value on Variable
21. Average Deviation (X i X ) =0 n
22. Mean Squared Deviation ( Xi X ) 2 n
23. The VariancePopulation 2Sample 2S
24. Variance ( X X ) 2S = 2 n 1
25. Variance The variance is given in squared units The
standard deviation is the square root of variance:
26. Sample Standard Deviation ( Xi X ) S= n1 2
27. Population Standard Deviation = 2
28. Sample Standard Deviation S= S 2
29. Sample Standard Deviation ( Xi X ) S= n1 2
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% 34.13% 34.13% 13.59%
2.14%2.14%
33. Normal Curve: IQ Example 70 85 100 115 145
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 -2 -1 0 1 2 z
37. The Standardized Normal is the Distribution of Z z +z
38. Standardized Scores x z=
39. Standardized Values Used to compare an individual value to
the population mean in units of the standard x deviation z=
40. Linear Transformation of Any Normal Variable Into a
Standardized Normal Variable X Sometimes the Sometimes thescale is
stretched scale is shrunk x z= -2 -1 0 1 2
41. Population distributionSample distributionSampling
distribution
42. Population Distribution x
43. Sample Distribution _ S X
44. Sampling Distribution X SX X
45. Standard Error of the Mean Standard deviation of the
sampling distribution
46. Central Limit Theorem
47. Standard Error of the Mean Sx = n
48. Distribution Mean Standard DeviationPopulation Sample S
XSampling X SX
49. Parameter Estimates Point estimates Confidence interval
estimates
50. Confidence Interval = X a small sampling error
51. SMALL SAMPLING ERROR = Z cl S X
52. E = Z cl S X
53. =X E
54. Estimating the Standard Error of the Mean S Sx = n
55. S = X Z cl n
56. Random Sampling Error and Sample Size are Related
59. Sample Size Formula - ExampleSuppose a survey researcher,
studyingexpenditures on lipstick, wishes to have a95 percent
confident level (Z) and arange of error (E) of less than $2.00.
Theestimate of the standard deviation is$29.00.
60. Sample Size Formula - Example (1.96 )( 29.00) 2 2 zs n= = E
2.00 2 56.84 = = ( 28.42 ) = 808 2 2.00
61. Sample Size Formula - ExampleSuppose, in the same example
as the onebefore, the range of error (E) isacceptable at $4.00,
sample size isreduced.
62. Sample Size Formula - Example ( 1.96)( 29.00) 2 2 zs n= = E
4.00 2 56.84 = = ( 14.21) = 202 2 4.00
64. Standard Error of the Proportion sp = pq n or p ( 1p )
n
65. Confidence Interval for a Proportion pZ S cl p
66. Sample Size for a Proportion Z pq2 n= E 2
67. z2pq n= 2 EWhere: n = Number of items in samplesZ2 = The
square of the confidence interval in standard error units. p =
Estimated proportion of success q = (1-p) or estimated the
proportion of failuresE2 = The square of the maximum allowance for
error between the true proportion and sample proportion or zsp
squared.
