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Class 4 - Conf. Interval Hyp. Test

Class 4 - Conf. Interval Hyp. Test - Point Estimation...

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Point Estimation Corresponding Sample Statistic Minimum Variance Unbiased Estimator Characteristic Parameter Best Estimate for the Parameter Mean μ y-bar or Proportion p p^ or Variance σ 2 s 2 The Mean & Proportion both location parameter The variance measures spre It is not a location param Confidence Interval Estimation Rather than estimating a parameter with a single value (point estimation), an can be created. The estimate is that the unknown parameter is in the interva on certain assumptions one can calculate the probability that the interval con unknown parameter value. This probability is the CONFIDENCE LEVEL a generally expressed as a percent. In practice, one specifies the confidence lev (probability) and then calculates the interval that would give this probability the sampling distribution of the statistic used to estimate the parameter. y p ˆ
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Best estimate plus or minus margin of error n are rs. ead. meter. n interval al. Based ntains the and is vel based on
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-4 0 -3.8 0 -3.6 0 -3.4 0 -3.2 0 -3 0 -2.8 0.01 -2.6 0.01 -2.4 0.02 -2.2 0.04 -2 0.05 -1.8 0.08 -1.6 0.11 -1.4 0.15 -1.2 0.19 -1 0.24 -0.8 0.29 -0.6 0.33 -0.4 0.37 -0.2 0.39 0 0.4 0.2 0.39 0.4 0.37 0.6 0.33 0.8 0.29 1 0.24 1.2 0.19 1.4 0.15 1.6 0.11 1.8 0.08 2 0.05 2.2 0.04 2.4 0.02 2.6 0.01 2.8 0.01 3 0 3.2 0 3.4 0 3.6 0 3.8 0 Confidence Level = 1 - α = 100*(1- α ) % Area in left tail = α /2 Area in right Cumulative area to the left = 1 - α / 2
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4 0
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t tail = α /2
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2-sided Table Value 2-tail 1-tail Cumulative Confidence Area Area Area Z 10 80% ### 0.1 0.9 1.282 1.372 90% ### 0.05 0.95 1.645 1.812 95% 5.00% 0.03 0.98 1.960 2.228 99% 1.00% 0.01 1 2.576 3.169 α = Alpha s used for σ 1 - α α α /2 1- α /2 Z 1 - α /2 t 1 - α /2 You can use the tables in the back of the book to obtain the Table Value. Remember that the t distribution with infinite degrees of freedom is iden normal distribution. You can use the t table, APPENDIX C (A-78), using freedom to obtain the values for the standard normal distribution. Excel can also be used to obtain these values as has been done to get the va For the standard normal or Z, use the NORMSINV(probability), where the cumulative probability = 1 - Alpha/2. You can also use NORMINV(proba For the t distribution, use the TINV(probability,df), where the probability probability = Alpha and df = degrees of freedom. If the variance (standard deviation) of sample data is used in the inference essentially used to estimate a phenomenon value. The t distribution with accounts for the extra variation that is introduced because of the sample m than the actual phenomenon value. If the inference process for either a hypothesis uses a variance or standard deviation calculated from sam used rather than the standard normal distribution.
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= Degrees of Freedom = df = n-1 Use INV function when you have a proba ntical to the standard the infinite degrees of alues above. e probability is the ability,0,1). y in this case is the two-tail e process then this value is h degrees of freedom = (n-1) measure of spread being used rather a confidence interval or a test of mple data then the t-distribution is
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ability and you want to get a value out that has that probability
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General Form for a Two-sided Confidence Interval for an Unknown Location Pa (Minimum Variance Unbiased Estimator of the Parameter) ± (2-sided Marg
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