Download - BR_Lec 20 & 21

Transcript
Page 1: BR_Lec 20 & 21

[email protected]

Lecture - 20Syed Far Abid Hossain

Determining the Size of a Sample

Page 2: BR_Lec 20 & 21

Sample Accuracy

[email protected]

Sample accuracy: refers to how close a random sample’s statistic (sign) is to the true population’s value it representsSample size is related to accuracy

Page 3: BR_Lec 20 & 21

How to Interpret Sample Accuracy

[email protected]

From a report…The sample is accurate ± 7% at the 95% level of confidence…

From a news articleThe accuracy of this survey is ± 7%…

Page 4: BR_Lec 20 & 21

How to Interpret Sample Accuracy

[email protected]

Interpretation Finding: 60% are aware of our brand

So… between 53% (60%-7%) and 67% (60%+7%) of the entire population is aware of our brand

Page 5: BR_Lec 20 & 21

[email protected]

There is only one method of determining sample size that allows the researcher to PREDETERMINE the accuracy of the sample results…

The Confidence The Confidence Interval Method of Interval Method of

Determining Sample Determining Sample SizeSize

Page 6: BR_Lec 20 & 21

The Confidence Interval Method of Determining Sample Size

[email protected]

This method is based upon the Confidence Interval and the Central Limit Theorem…

Confidence interval: range whose endpoints define a certain percentage of the response to a question

Page 7: BR_Lec 20 & 21

Review: What does sample accuracy mean?

[email protected]

ExampleSample size of 1,000Finding: 40% of respondents like our brand

Sample accuracy is ± 3% (via our formula)

Page 8: BR_Lec 20 & 21

Sample Size Formula

[email protected]

Fortunately, statisticians have given us a formula which is based upon these relationships.The formula requires that we

Specify the amount of confidence we wish (95%)

Estimate the variance in the populationSpecify the amount of desired accuracy

we want.When we specify the above, the formula

tells us what sample we need to use…

Page 9: BR_Lec 20 & 21

Question

[email protected]

***What is Sample Accuracy? How to Interpret Sample Accuracy? Give an example assuming 95% confidence level.

Page 10: BR_Lec 20 & 21

Lecture – 21Syed Far Abid HossainSample Size Formula

[email protected]

Page 11: BR_Lec 20 & 21

Sample Size Formula

[email protected]

Standard sample size formula for estimating a percentage:

Page 12: BR_Lec 20 & 21

Estimating a Percentage: What is n?

[email protected]

Z=1.96 (95% confidence)p=42q=100-p=58e=5What is n?

Page 13: BR_Lec 20 & 21

Special Sample Size Determination Situations

[email protected]

Sampling from small populations:Small population: sample exceeds 5% of total population size

Page 14: BR_Lec 20 & 21

Special Sample Size Determination Situations

[email protected]

Sample size using nonprobability sampling:When using nonprobability sampling, sample size is unrelated to accuracy, so cost-benefit considerations must be used.

Page 15: BR_Lec 20 & 21

Practice Examples

[email protected]

5a. Using the formula provided in your text, determine the approximate sample sizes for each of the following cases, all with precision (allowable error) of ±5%:Variability of 30%, confidence level of 95%

(323) 322.6 =25

8064 =

252100 x 3.84 =

570) x (30961. =

e(pq)z = n

2

2

2

2

Page 16: BR_Lec 20 & 21

Practice Examples

[email protected]

5b. Using the formula provided in your text, determine the approximate sample sizes for each of the following cases, all with precision (allowable error) of ±5%:Variability of 60%, confidence level of 99%

(639) 639.4 =25

15,984 =

252400 x 6.66 =

540) x (60582. =

e(pq)z = n

2

2

2

2

Page 17: BR_Lec 20 & 21

Practice Examples

[email protected]

5c. Using the formula provided in your text, determine the approximate sample sizes for each of the following cases, all with precision (allowable error) of ±5%:Unknown variability, confidence level of 95%

384 =25

9600 =

252500 x 3.84 =

550) x (50961. =

e(pq)z = n

2

2

2

2