This activity is drawn from Mario Triola's Elementary Statistics, 10° ed., p.380, 2008. The bootstrap method can be used

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This Activity Is Drawn From Mario Triola S Elementary Statistics 10 Ed P 380 2008 The Bootstrap Method Can Be Used 1 (83.03 KiB) Viewed 44 times

This Activity Is Drawn From Mario Triola S Elementary Statistics 10 Ed P 380 2008 The Bootstrap Method Can Be Used 2 (83.03 KiB) Viewed 44 times

This Activity Is Drawn From Mario Triola S Elementary Statistics 10 Ed P 380 2008 The Bootstrap Method Can Be Used 3 (49.04 KiB) Viewed 44 times

This activity is drawn from Mario Triola's Elementary Statistics, 10° ed., p.380, 2008. The bootstrap method can be used to construct confidence intervals for situations in which traditional methods cannot (or should not) be used. For example, the following sample of 10 values was randomly. selected from a population with a distribution that is very far from normal, so any methods requiring a normal distribution should not be used. 2.9 564.2 1.4 4.7 67.6 4.8 51.3 3.6 18.0 3.6 If we want to use the above sample data for the construction of a confidence interval estimate of the population mean, we note that the sample is small, and there is an outlier. The bootstrap method, which makes no assumptions about the original population, typically requires a computer to build a bootstrap population by replicating (duplicating) a sample many times. We can draw from the sample with replacement, thereby creating an approximation of the original population. In this way, we pull the sample up "by it's own bootstraps" to simulate the original population. Using the sample data given above, construct a 95% confidence interval estimate of the population mean by using the bootstrap method. 1. STATDISK Go to www.triolastats.com and click on "Access Statdisk (Free)" at the top of the page. You may need to set up an account using email to do this. 2. DATA Enter the 10 sample values in column 1 of the Data Window. 3. BOOTSTRAP RESAMPLING Go to Analysis, under the main menu and select Bootstrap Resampling (near the bottom). Create 500 new samples of column 1. You should now see means in column 2 and standard deviation in column 3. 4. SORT DATA The first item under "Data" at the top of the screen should be "Sort Data." Do that. You can also use the green "Sort" button at the top right. 5. 95% CONFIDENCE INTERVALS You can now create a 95% CI by finding P2.5 and P97.5 for the mean and standard deviation. Record your values below: << <o< 6. DID IT WORK? The true standard deviation is a = 232.1. Was your confidence interval effective?

7. Cl for Variance with Assumptions Not Met Consider a sample of 44 HHP 295 student ages below: 1888999999 2 0000012222233333 2 577889 3 000122 3 67 4 003 4 503 1-Var Stats X-26.40909091 Ex=1162 Ex2=33868 Sx-8.600481819 ox-8.50218737 +n=44 Ignoring the skewed nature of the distribution would lead to the following confidence interval on the variance: 40.0 ² 153.6 However, the procedure for estimating variances requires normality even if n > 30 (recall the Central Limit Theorem only applies to means, not variances.) Use the Bootstrap procedure to create a valid confidence interval on the population variance using the techniques on the previous page. Start by clearing out the data in Statdisk ("Clear" menu item at the top of the screen) and entering the 44 values for this data set (18, 18, etc.). <0² <.