1. Sample size

2. Ch 132 Sample Size Formula Standard sample size formula for estimating a percentage:

3. Ch 133 Practical Considerations in Sample Size Determination 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?

4. Ch 134 Practical Considerations in Sample Size Determination How to determine the amount of desired sample error – Researchers should work with managers to make this decision. How much error is the manager willing to tolerate? – Convention is + or – 5% – The more important the decision, the more (smaller number) the sample error.

5. Ch 135 Practical Considerations in Sample Size Determination How to decide on the level of confidence desired – Researchers should work with managers to make this decision. The more confidence, the larger the sample size. – Convention is 95% (z=1.96) – The more important the decision, the more likely the manager will want more confidence. 99% confidence, z=2.58.

6. Ch 136 Example Estimating a Percentage in the Population 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 65% confident that the survey estimate will be within ±5% of the true percentage of “aware” consumers in the population. – What is n?

7. Ch 137 Estimating a Percentage: What is n? Z=1.96 (95% confidence) p=42 q=100-p=58 e=5 What is n?

8. Ch 138 Estimating a Percentage: What is n? What does this mean? – It means that if we use a sample size of 374, after the survey, we can say the following of the results: (assume results show that 55% are aware) – “Our most likely estimate of the percentage of consumers that are ‘aware’ of our brand name is 55%. In addition, we are 95% confident that the true percentage of ‘aware’ customers in the population falls between 50% and 60%.” N=374

9. Ch 139 Estimating a Mean Estimating a mean requires a different formula (See MRI 13.2, p. 378) Z is determined the same way (1.96 or 2.58) E is expressed in terms of the units we are estimating (i.e., if we are measuring attitudes on a 1-7 scale, we may want error to be no more than ±.5 scale units S is a little more difficult to estimate…

10. Ch 1310 Estimating s Since we are estimating a mean, we can assume that our data are either interval or ratio. When we have interval or ratio data, the standard deviation, s, may be used as a measure of variance.

11. Ch 1311 Estimating s How to estimate s? – Use standard deviation from a previous study on the target population. – Conduct a pilot study of a few members of the target population and calculate s. – Estimate the range the value you are estimating can take on (minimum and maximum value) and divide the range by 6.

12. Ch 1312 Estimating s – Why divide the range by 6? The range covers the entire distribution and ± 3 (or 6) standard deviations cover 99.9% of the area under the normal curve. Since we are estimating one standard deviation, we divide the range by 6.

13. Ch 1313 Example Estimating the Mean of a Population What is the required sample size? – Management wants to know customers’ level of satisfaction with their service. They propose conducting a survey and asking for satisfaction on a scale from 1 to 10. (since there are 10 possible answers, the range=10). – Management wants to be 99% confident in the results and they do not wan the allowed error to be more than ±.5 scale points. – What is n?