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# quiz 2 cheat sheet.docx

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Michael Rochon

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Chapter #10: ESTIMATION - Test statistics- actual applications using the formulas on flow chart to Two population mean: we use the statistic Xbar1- Xbar2 Statistical inference- acquires info and draw conclusion about population determine results and using results to see if it falls in the rejection Two cases: samples regions to make conclusion - two unknown population variances are equal Estimation- objective is to determine value of population parameter using - P-value-can only find p-value manually when your dealing with z - two unknown population variances are not equal sample statistics distribution You must do an F-TEST before you can tell if the variances are equal or not in an Sample mean (Xbar) and estimate population mean (mu) o P-value of a test is probability of observing a test statistiindependent sample situation. TWO types of inferences at least as extreme as the one computed, given that null - Estimation and hypothesis testing hypothesis is true. TWO types of estimator o The smaller the p value the more statistical evidence exists - Point estimator- value unknown parameter using SINGLE VALUE OR PT to support alternative hypotheis.  Three drawbacks o Ex. Given mu=170 extreme values or Xbar= 178 o Virtually certain that estimate will be wrong ,P(z>178-170/ 65/root 400)=1-0.9931=0.0069 o Need to know how close to estimator is to parameter - Conclusion – statement about whether there is enough evidence and o Do not reflect larger sample size or parameter value information to make assumptions or not in accordance to the - Interval estimator (confidence interval)- draws inferences about population by confidence level. estimating value of unknown parameter using interval EXAMPLE: Qualities of Estimators- unbiased, consistency, relative efficiency - Unbiased estimator- expected value is equal to parameter E(X)=MU (cant tell how close to parameter) - Consistency estimator- difference between estimator and parameter grows smaller as ample gets larger - Relative efficient estimator- if there are 2 unbiased estimators of a parameter, the 1 variance smaller is said to have relative efficient Chapter 12: Inference about one population The width of confidence interval When σ is unknown we conduct a t-test and estimator on mu where z becomes t - Larger confidence level produces wider confidence intervals and σ becomes s in the equations. - Larger value of σ produce wider confidence intervals The degrees of freedom – (a function of sample size) determines how spread the - Larger sample size, narrow confidence interval distribution is (compared to the normal distribu
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