STATISTICS FOR MANAGERS

II. Inferential Statistics

A. Confidence Interval Estimation

1. Point estimation

• Estimate a single point

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2. Confidence intervals

• Range of numbers constructed around a point estimate

• Probability that confidence interval contains population parameter is known

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3. Confidence interval for the population mean

• Use sample mean as a point estimate

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a. Standard deviation known

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b. Standard deviation unknown

• Use sample standard deviation to estimate population standard deviation

• Appropriate probability distribution is Student’s t if underlying population is normal or sample size is large

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• Degrees of freedom

- Sample mean needs to be estimated when calculating the sample variance, reducing freedom of sample values to vary

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• Confidence interval

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• Gas Mileage

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c. Use of Excel and PHStat

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4. Confidence interval for the population proportion

• Use p as a point estimate

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• Nielsen television ratings

• Use of PHStat:

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• Pew Research Center Methodology

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5. Sample size determination

• Want to determine sample size needed to give a confidence interval of a certain width

a. Mean

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b. Proportion

(1) Information on proportion

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(2) No information on proportion

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6. Ethical issues

• Confidence interval estimates (or margin of error) should be given along with point estimate - also confidence level, sample size, and interpretation