1. Essentials of Marketing Research William G. Zikmund
Chapter 13:
Determining 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,
$3,000 - $4,
$5,000 - $9,
$10,000 - $14,
$15,000 or more
3,120

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

9. Probability Distribution of Amounts of Deposits
Amount Probability
less than $3,
$3,000 - $4,
$5,000 - $9,
$10,000 - $14,
$15,000 or more
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
Salesperson Sales calls
Mike
Patty
Billie
Bob
John
Frank
Chuck
Samantha 26

14. Sales for Products A and B, Both Average 200
Product A Product B

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 Dispersion5 4 3 2 1
Low Dispersion
Frequency
Value on Variable

20. Low Dispersion Verses High Dispersion5 4 3 2 1
High dispersion
Frequency
Value on Variable

21. Average Deviation

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 Conventional Product Adoption Life Cycle:
Five types of customers who will end up adopting a product
INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview.
EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release.
EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters.
LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar.
LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video.
MEAN

32. Normal Distribution 13.59% 13.59% 34.13% 34.13% 2.14% 2.14%
Conventional Product Adoption Life Cycle:
Five types of customers who will end up adopting a product
INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview.
EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release.
EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters.
LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar.
LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video.
2.14%
2.14%

33. Normal Curve: IQ Example70 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
Conventional Product Adoption Life Cycle:
Five types of customers who will end up adopting a product
INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview.
EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release.
EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters.
LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar.
LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. z 1 2 -2 -1

37. The Standardized Normal is the Distribution of 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 VariableX m
Sometimes the
scale is stretched
Sometimes the
scale is shrunk

41. Population distribution
Sample distribution
Sampling distribution

42. Population Distribution
Conventional Product Adoption Life Cycle:
Five types of customers who will end up adopting a product
INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview.
EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release.
EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters.
LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar.
LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. -s m s x

43. Sample Distribution _ C X S Conventional Product Adoption Life Cycle:
Five types of customers who will end up adopting a product
INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview.
EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release.
EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters.
LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar.
LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. _ C X S

44. Sampling Distribution
Conventional Product Adoption Life Cycle:
Five types of customers who will end up adopting a product
INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview.
EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release.
EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters.
LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar.
LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video.

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

46. Central Limit Theorem

47. Standard Error of the Mean

49. Parameter Estimates
Point estimates
Confidence interval estimates

50. Confidence Interval

54. Estimating the Standard Error of the Mean

56. Random Sampling Error and Sample Size are Related

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

58. Sample Size Formula

59. 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.

60. Sample Size Formula - Example

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

62. Sample Size Formula - Example

63. Calculating Sample Size
99% Confidence [ ]
1389 =
265 . 37 2 53 74 ú û ù ê ë é ) 29 )( 57 ( n
347
6325 18 4

64. Standard Error of the Proportion

65. Confidence Interval for a Proportion

66. Sample Size for a Proportion

67. E pq z n = Where: n = Number of items in samples2 E pq z n =
Where:
n = Number of items in samples
Z2 = The square of the confidence interval
in standard error units.
p = Estimated proportion of success
q = (1-p) or estimated the proportion of failures
E2 = The square of the maximum allowance for error
between the true proportion and sample proportion
or zsp squared.

68. Calculating Sample Size at the 95% Confidence Level
753 =
001225 .
922 ) 24
)(.
8416 3 (
035
( . 4 6 (. 96 1. n q p 2