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# Bmgt 311 chapter_10

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### Bmgt 311 chapter_10

1. 1. BMGT 311: Chapter 10 Determining the Size of a Sample 1
2. 2. Learning Objectives • To understand the eight axioms underlying sample size determination with a probability sample • To know how to compute sample size using the conﬁdence interval approach  • To become aware of practical considerations in sample size determination • To be able to describe different methods used to decide sample size, including knowing whether a particular method is ﬂawed 2
3. 3. 3
4. 4. 4
5. 5. Key Points • Many managers falsely believe that sample size and sample representativeness are related, but they are not. • A sample size decision is usually a compromise between what is theoretically perfect and what is practically feasible. • Many practitioners have a large sample bias, which is the false belief that sample size determines a sample’s representativeness. 5
6. 6. Important Points about Sampling • Sampling method (not sample size) is related to representativeness. • Only a probability sample (random sample) is truly representative of a population. • Sample size determines accuracy of ﬁndings. • The only perfect accurate sample is a census - which is for the most part, not positive in Marketing Research 6
7. 7. Sample Accuracy • Sample accuracy: refers to how close a random sample’s statistic is to the true population’s value it represents 7
8. 8. Page 239 8
9. 9. Two Types of Error • Non sampling error: pertains to all sources of error other than sample selection method and sample size • Sampling error: involves sample selection and sample size 9
10. 10. Sample Size and Accuracy • Which is of these is more accurate? • A large probability sample or • A small probability sample? • The larger a probability sample is, the more accurate it is (less sample error). 10
11. 11. Page 240 11
12. 12. Page 241 12
13. 13. Sample Error • Variability refers to how similar or dissimilar responses are to a given question. 13
14. 14. Sample Error 14
15. 15. The Conﬁdence Interval Method of • Conﬁdence interval approach: applies the concepts of accuracy, variability, and conﬁdence interval to create a “correct” sample size • The conﬁdence interval approach is based upon the normal curve distribution. • We can use the normal distribution because of the Central Limit Theorem. 15
16. 16. Central Limit Theorem • Since 95% of samples drawn from a population will fall within + or – 1.96 × sample error (this logic is based upon our understanding of the normal curve), we can make the following statement . . . • If we conducted our study over and over, 1,000 times, we would expect our result to fall within a known range. Based upon this, we say that we are 95% conﬁdent that the true population value falls within this range. 16
17. 17. Example - Page 243 17
18. 18. Figuring out the Sample Error - Module 1 Handout • n Values: • n = 1,000 • n = 500 • n = 100 • n = 50 • p and q = 50 • Conﬁdence Interval = 95% or 1.96 18
19. 19. Figuring out the Sample Error - Module 1 Handout • n Values: • n = 1,000 Sample Error _____ • n = 500 Sample Error _____ • n = 100 Sample Error _____ • n = 50 Sample Error _____ • p and q = 50 • Conﬁdence Interval = 95% or 1.96 19
20. 20. 20
21. 21. Sample Size Formula • Need to know • Variability: p × q • Acceptable margin of sample error: e • Level of conﬁdence: z 21
22. 22. Standard Sample Size Formula 22
23. 23. Example: Estimating a Sample Size • What is the required sample size? • Five years ago, a survey showed that 42% of consumers were aware of the company’s brand (Consumers were either “aware” or “not aware.”) • After an intense ad campaign, management wants to conduct another survey and they want to be 95% conﬁdent that the survey estimate will be within ±5% of the true percentage of “aware” consumers in the population. • What is n? 23
24. 24. Example: Estimating a Sample Size • Five years ago, a survey showed that 42% of consumers were aware of the company’s brand (Consumers were either “aware” or “not aware.”) • After an intense ad campaign, management wants to conduct another survey and they want to be 95% conﬁdent that the survey estimate will be within ±5% of the true percentage of “aware” consumers in the population. • Z=1.96 (95% conﬁdence) • p=42 • q=100-p=58 • e=5 • What is n? • 24
25. 25. Example: Estimating a Sample Size • Five years ago, a survey showed that 42% of consumers were aware of the company’s brand (Consumers were either “aware” or “not aware.”) • After an intense ad campaign, management wants to conduct another survey and they want to be 95% conﬁdent that the survey estimate will be within ±5% of the true percentage of “aware” consumers in the population. • Z=1.96 (95% conﬁdence) • p=42 • q=100-p=58 • e=5 • What is n? • n = 374 25
26. 26. Chapter 10 Handout Module 2, Figure out n 26
27. 27. First Step = Figure out z and q Situation Conﬁdence Level Value of z p q (100-p) Allowable Error 1 95% 1.96 65 35 3.5 2 99% 2.58 65 35 3.5 3 95% 1.96 60 40 5 4 99% 2.58 60 40 5 5 95% 1.96 50 50 4 27
28. 28. Example 1: Page 247 28
29. 29. Example 2: Page 247 29
30. 30. Practical Considerations • How to estimate variability (p times q) in the population? • Expect the worst cast (p = 50; q = 50) • Estimate variability • Previous studies? • Conduct a pilot study? 30
31. 31. Practical Considerations • How to determine the amount of acceptable sample error. • Researchers should work with managers to make this decision. How much error is the manager willing to tolerate? • See page 251 for practical example • Researchers should work with managers to take cost into consideration in this decision. 31
32. 32. Practical Considerations • How to decide on the level of conﬁdence to use. • Researchers typically use 95% or 99%. • Most clients would not accept a conﬁdence interval below 95% as a representative of the overall population 32
33. 33. Other Methods of Sample Size Determination • Arbitrary “percentage rule of thumb” • Conventional sample size • Statistical analysis approach requirements • Cost basis 33
34. 34. Sampling from Small Populations • With small populations, use the ﬁnite population multiplier to determine small size. 34
35. 35. Example: Page 255 35
36. 36. Example: Page 255 36
37. 37. More Practice for Test Questions • Page 258 - Question #13 - Crest Toothpaste Sample Size • Page 247 - Sample Size Calculations Practice • Make sure you practice and know all of the equations discussed in class • Sample Size Margin of Error • Sample Size Formula • Small Population Formula 37