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Download • Sample Distritubion distribution that specifies probabilities for the possible values
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• Sample Distritubion The sample distribution of a statistic is the probability distribution that specifies probabilities for the possible values the statistic can take. • Mean and Standard Error of Sampling Distribution of Sample Mean x̄ For a random sample of size n from a population having mean µ and standard deviation σ, the sampling distribution of the sample mean x̄ has mean = µ and σ standard deviation = √ . n We call the standard deviation of a sampling distribution a standard error. • Mean and Standard Deviation of the Sample Distribution of a Proportion For a random sample of size n from a population with proportion p of outcomes in a particular category, the sampling distribution of the proportion of the sample in that category has r p(1 − p) . mean = p and standard deviation = n We call the standard deviation of a sampling distribution a standard error. sample statistics sample mean x̄ sample s.d. s sample proportion p̂ ←→ ←→ ←→ ←→ −→ population parameters population mean µ population s.d. σ population proportion p • Population distribution • Data distribution • Sampling distribution • Central Limit Theorem (Approximately Normal Sampling Distribution for Sample Mean x̄) For random sampling with a large sample size n, the sampling distribution of the sample mean x̄ is approximately a normal distribution.
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