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Statistical Inference1

# Statistical Inference1 - Statistical Inference branch of...

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Statistical Inference : branch of statistics that has to do with using samples to guess/infer information about unknown populations, most notably, inferring about parameters of unknown populations such as population means and population proportions Point estimate : a single # calculated from a sample to guess a population parameter ( for example x is the point estimator for µ A (1-α)100% confidence interval is a range of #’s characterized by a lower bound and upper bound that gives a range of likely values for a population parameter. 90%=1.645=α:.10. 95%=1.96=α:.05. 98%=2.33=α:.02. 99%=2.58=α:.01 95% CI for µ is given by ± . x 1 96sn Sample Variance: = - - s2 xi1 xi2nn 1 Hypothesis test: a means of deciding when two complimentary statements about a population parameter. The null hypothesis ( Ho ) always states that the population parameter is equal to some hypothesized value (ie. Ho : µ=5) The alternative hypothesis ( Ha ) always involves some form of inequality. ( <, ≠, >) When Ha involves ≠, the test is 2-tailed, otherwise the test is 1 tailed. If ≠, then the test is 2-tailed, otherwise the test is 1-tailed. Type I error: rejecting the null hypothesis when it is really true. Type II error: not rejecting null hypothesis when null hypothesis is really false Large sample   test about   population   mean  µ For large sample tests, our point estimates for the population parameter will have a normal distribution. Usually, we want to test whether the population parameter (µ) is equal to some hypothesized value ( ) µo 1) Ho: 2) The Zts = - x μosn Notice that if the sample mean ( x ) is close to the hypothesized value ( ) μo then Zts will be close to 0. If x is far from μo then Zts will be far from 0. 3) Next Ie. For 1 tail test w/ Zts = 3.12 For 2 tail test w/ Steps for a small sample test about population mean  µ When the sample size is small the test statistic no longer has a std. normal dist’n. instead it will have a t dist’n w/ some degrees of freedom 1) Ho:  : µ = μo Ha= µ≠ μo

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Statistical Inference1 - Statistical Inference branch of...

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