# lect16 - Margin of Error Concepts of Statistical Tests...

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Margin of Error Concepts of Statistical Tests Outline Margin of Error Determining Sample Size Confidence Intervals for Quantities Related to μ or p Concepts of Statistical Tests 1 / 15 ISOM 2500 Lect 16: CI-Sample Size; Concepts of Tests

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Margin of Error Concepts of Statistical Tests Determining Sample Size Confidence Intervals for Quantities Re Margin of Error Recall 95% CI: h ¯ x ± 2 s n i for mean and ˆ p ± 2 q ˆ p ( 1 - ˆ p ) n for proportion. The extent of the confidence interval to either side of the estimated value is called the margin of error (ME) . For mean, ME = 2 s n at 95% confidence level For proportion, ME = 2 q ˆ p ( 1 - ˆ p ) n at 95% confidence level There’re three factors determining the margin of error: Level of confidence Variation of the data Number of observations Sometimes we want a small margin of error while maintaining a high confidence level. How to achieve such a goal? 2 / 15 ISOM 2500 Lect 16: CI-Sample Size; Concepts of Tests
Margin of Error Concepts of Statistical Tests Determining Sample Size Confidence Intervals for Quantities Re Determining Sample Size in the case of Means: Diet case A nutritionist wants to know the average calories intake for female customers to within ± 50 calories with 95% confidence. Can we determine how large a sample we need to obtain such an accuracy? Required: ME 50. We know that ME = 2 s n , if we knew s , then n should be such that n 4 s 2 50 2 , but we don’t know the sample standard deviation s , since we haven’t collected the sample yet. Hence we need to have a pilot sample , i.e., a small sample of, say, 10 to 30 cases used to learn about the variation. A pilot study gives a standard deviation 430 calories. Answer the above question, find n . n = 295 . 8 The company thus should survey about 300 customers. 3 / 15 ISOM 2500 Lect 16: CI-Sample Size; Concepts of Tests

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Margin of Error Concepts of Statistical Tests Determining Sample Size Confidence Intervals for Quantities Re Determining Sample Size in the case of proportions: Brand awareness Case Suppose we’re doing a survey of brand awareness. We need the survey to have a margin of error of 3% or less (with 95% confidence).
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• Spring '11
• a
• Null hypothesis, Statistical hypothesis testing, Statistical tests, Type I and type II errors, CI-Sample Size, Error Concepts

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