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Chapter 11

# Chapter 11 - Chapter 11 • A parameter in a statistical...

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Unformatted text preview: Chapter 11 • A parameter in a statistical problem is a number that describes a population , such as the population mean σ To estimate an unknown parameter , use a statistic calculated from a sample , such as the sample mean • The law of large numbers states that the actually observed mean outcome must approach the mean μ of the population as the number of observations increases. • The population distribution of a variable describes the values of the variable for all individuals in a population . • The sampling distribution of a statistic describes the values of the statistic in all possible samples of the same size from the same population . • When the sample is an SRS from the population , the mean of the sampling distribution of the sample mean is the same as the population mean . That is, μ is an unbiased estimator of μ . • The standard deviation of the sampling distribution of is σ / foran SRS of size n if the population has standard deviation σ . That is, averages are less variable than individual observations. • When the sample is an SRS from a population that has a Normal distribution , the sample mean alsohas a Normal distribution . Choose an SRS of size n from any population with mean μ and finite standard deviation σ . The central limit theorem states that when n is large the sampling distribution of is approximately Normal. That is, averages are more Normal than individual observations. We can use the N ( μ, σ / distribution to calculate approximate probabilities for events involving . 11.1 Effects of caffeine. How does caffeine affect our bodies? In a matched pairs experiment , subjects pushed a button as quickly as they could after taking a caffeine pill and also after taking a placebo pill. The mean pushes per minute were 283 for the placebo and 311 for caffeine. Is each of the boldface numbers a parameter or a statistic? Correct Answer Both are statistics . 11.3 Ancient projectile points. Most of what we know about North America before Columbus comes from artifacts such as fragments of clay pottery and stone projectile points. Locations and cultures can be distinguished by the types of artifacts found. At one site in North Carolina, 82% of the projectile points unearthed came from the Middle Archaic period (6000 to 3000 B.C.) and the remaining 18% from the Late Archaic period (3000 to 1000 B.C.). Is each of the boldface numbers a parameter or a...
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Chapter 11 - Chapter 11 • A parameter in a statistical...

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