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Population distribution parameter sampling

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Unformatted text preview: ting the value of an unknown parameter using a single value or point. Population distribution Parameter ? Sampling distribution Point estimate Slide 5 Interval Estimate An interval estimate draws inferences about a population by estimating the value of an unknown parameter using an interval. Population distribution Sample distribution Parameter Interval estimate Slide 6 Interval Estimation of a Population Mean: Large­Sample Case s s Calculating an Interval Estimate: Large­Sample Case with σ Known Known Calculating an Interval Estimate: Large­Sample Case with σ Unknown Unknown Slide 7 Estimating the Population Mean when the Population Variance is Known s How is an interval estimate produced from a sampling distribution? • A sample of size n is drawn from the population, and its mean is calculated. x x • By the central limit theorem is normally distributed (or approximately normally distributed.), thus… Slide 8 Estimating the Population Mean when the Population Variance is Known s For sufficient large sample size (n ≥ 30) s We have established in the last topic that x− µ Z= σn P(µ − zα 2 σ σ ≤ x ≤ µ + zα 2 )= 1− α n n Slide 9 The Confidence Interval for µ ( σ is known) s This leads to t...
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