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Lecture - 20Syed Far Abid Hossain

Determining the Size of a Sample

Sample Accuracy

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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

How to Interpret Sample Accuracy

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

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

How to Interpret Sample Accuracy

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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

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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

The Confidence Interval Method of Determining Sample Size

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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

Review: What does sample accuracy mean?

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

Sample accuracy is ± 3% (via our formula)

Sample Size Formula

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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…

Question

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

Lecture – 21Syed Far Abid HossainSample Size Formula

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Sample Size Formula

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Standard sample size formula for estimating a percentage:

Estimating a Percentage: What is n?

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

Special Sample Size Determination Situations

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

Special Sample Size Determination Situations

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

Practice Examples

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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

Practice Examples

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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

Practice Examples

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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