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Unformatted text preview: 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: CISample Size; Concepts of Tests 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: CISample 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: CISample 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 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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This note was uploaded on 12/20/2011 for the course ACCT/MGMT 2010 taught by Professor A during the Spring '11 term at HKUST.
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