handout_6_1 - 6.1 Estimating with Confidence those who took...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
6.1 Estimating with Confidence those who took the SAT math in 2003: mean= 519, sd= 115 give test to SRS of 500 California students: x = 461 (math) What can you say about the mean score μ in population of 385,000? x is an unbiased estimator of μ ( x μ = μ) • but how reliable is this estimate? (how variable is the statistic?) recall x is approximately N (μ, n σ ) when n is large suppose σ = 100, then x = 4.5 (unrealistic to assume we would know σ- CH 7) x has normal distribution centered at unknown population mean μ with x = 4.5 Figure 6.2 •the 68-95-99.7 rule says that, for any N distribution, 95% of observations within 2 sd of mean •95% chance→ x will be within 2 standard deviations of x •95% chance→ x will be within 9 points of population mean μ •to say that x lies within 9 points of μ is the same as saying that μ is within 9 points of x •so 95% of all samples will capture the true μ in the interval from x - 9 to x + 9 our sample gave x = 461 95% confidence interval= x ± 9 461 ± 9 [452, 470] we say that we are 95% confident that the unknown mean score lies between [452, 470]
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
our sample gave x = 461 95% confidence interval= x ± 9 461 ± 9 [452, 470] we say that we are 95% confident that the unknown mean score lies between [452, 470] Once we look at a sample and construct a confidence interval, there are two possibilities: 1) The interval between 452 and 470 contains the true population mean μ Our sample is one of the 95% of samples where μ lies within 9 points of x . 2) The true population mean μ is not contained between 452 and 470 (rare result).
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

handout_6_1 - 6.1 Estimating with Confidence those who took...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online