Week 6 outline
Week 6 outline STA3032
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This 2 page Class Notes was uploaded by Tia Belvin on Saturday March 5, 2016. The Class Notes belongs to STA3032 at University of Florida taught by Demetris Athienitis in Spring 2016. Since its upload, it has received 24 views. For similar materials see Engineering Statistics in Engineering and Tech at University of Florida.
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Date Created: 03/05/16
3.3 INFERENCE FOR POPULATION VARIANCE 1) We can calculate the estimated population variancewith 2) also note that this is true: 2 *where X is representative of the chi square distribution with n-1 degrees of freedom 3.3.1 CONFIDENCE INTERVAL 3.3.2 HYPOTHESIS TEST 2 1) To test something dealing with σ we use test statistic: where the null hypothesis is still rejected when p-value<α 3.4 DISTRIBUTION FREE INTERFERENCE 1) When using small sample sizes: a. We cannot assume normally distributed data b. We need to use exact nonparametric procedures whenfinding statistics c. Instead of means we will use medians because they are less influenced by outliers 3.4.1 SIGN TEST 1) Recall that a pth percentile includes all data thatfalls above (1-p)% a. Let B denote the number of observations greater than the pth percentile 2) B~Bin(n,1-p) where µ depotes the population pth percentile 3) We can test hypotheses dealing with µ p a. The p-value must still be smaller than α to rejectthe null hypothesis 3.4.2 WILCOXON SIGNED-RANK TEST 1) In this case, the null hypothesis is that the distribution of data is centrally located around a certain value µ0. This value Is tested against X. a. The test determines whether Xs tend to be larger, smaller, or different than µ . 0 2) To carry out the test: a. Center the data according to the null hypothesis bycalculating the differences between your data values (X) and µ 0 b. Rank the absolute values of the differences c. Calculate the test statistic,s+ , by adding all off differences 3) Note: 4) The test statistic, denoted by W:
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