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ch5 notes - Statistical Inference drawing conclusions about...

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Statistical Inference drawing conclusions about a population, based on a sample. uses properties of the sampling distribution and random sampling. Example : Population: GRE results for a new exam format on the quantitative section Sample: n=300 test scores Population Sampling Dist. for X shape normal? approx. normal mean μ (unknown) μ SD σ =100 (assume known) 100 5.8 300 X n == = ~95% of the Sampling Distribution is within 2 X ± i of μ . 1) In ~95% of the samples of n=300, X is within +/- 11.6 pts of μ . 2) In ~95% of the samples of n=300, μ is within +/- 11.6 pts of X . 3) In ~95% of the samples of n=300, μ lies between 11.6 11.6 Xa n d X −+ . 4) We are ~95% confident that we have one of the samples that gives an interval containing μ .

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Hypothesis Testing Null Hypothesis (H o ): The population mean is 54 cm. Alternative Hypothesis (H A ): The population mean is greater than 54 cm. p-value Measures the strength of the sample evidence against H o A small p-value gives strong evidence against H o Definition : The probability, computed assuming that H o is true, of a sample result ( X ) as extreme or more extreme than the one from our sample. Rule of Thumb for the significance of p-values If the p-value is less than .05, then our results are statistically significant at the .05 level H o : μ=54 cm 4.5 1.5 9 X cm cm σ == H a : μ>54 a = 58) α = .05 4 Steps for finding the Power in a test of hypotheses 1) Write the RR for H o
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This note was uploaded on 03/19/2012 for the course GEOG 305 taught by Professor Prout during the Spring '08 term at Texas A&M.

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ch5 notes - Statistical Inference drawing conclusions about...

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