Hypothesis Test: Standard Deviation or Variance Access tech supplements, videos, and data sets at www.TriolaStats.com/ES13 TECH CENTER continued R R command not available at time of publication. R is rapidly evolving, and an updated list of statistical commands is available at TriolaStats.com. Excel XLSTAT Add-In (Required) Requires original sample data; does not work with summary data. 1. Click on the XLSTAT tab in the Ribbon and then click Parametric tests. 2. Select One-sample variance test from the dropdown menu. 3. Under Data enter the range of cells containing the sample data. For Data format select One column per sample. If the first row of data contains a label, also check the Column labels box. 4. For Range, enter a cell location such as D5 where the results will be displayed. 5. Click the Options tab. 6. Under Alternative hypothesis select the desired format (3 for two-tailed test, * for left-tailed test, + for right-tailed test). 7. For Theoretical variance, enter the claimed value of the population variance. Enter the desired significance level (enter 5 for a significance level of 0.05). 8. Click OK to display the results. The test statistic is identified as Chisquare (Observed value). The P-value is also displayed. TIP: The above procedure is based on testing a claim about a population variance; to test a claim about a population standard deviation, use the same procedure and enter s2 for the Theoretical Variance. Statistical Literacy and Critical Thinking 1.Minting Dollar Coins Assume that the U.S. Mint manufactures dollar coins so that the standard deviation is 0.04000 g (based on Data Set 40 “Coin Weights” in Appendix B). Listed below are weights (grams) of dollar coins manufactured with a new process designed to decrease the standard deviation so that it is less than 0.04000 g. This sample has these summary statistics: n = 16, x = 8.06576g, s = 0.02176g. If we want to use a 0.05 significance level to test the claim that the sample is from a population with a standard deviation less than 0.04000 g, what requirements must be satisfied? How does the normality requirement for a hypothesis test of a claim about a standard deviation differ from the normality requirement for a hypothesis test of a claim about a mean? 8.0652 8.0548 8.0754 8.0545 8.0334 8.0126 8.0758 8.0517 8.0730 8.1084 8.0678 8.0808 8.0680 8.0818 8.0684 8.0806 2.Minting Dollar Coins Use the data and the claim given in Exercise 1 to identify the null and alternative hypotheses and the test statistic. What is the sampling distribution of the test statistic? 3. Minting Dollar Coins For the sample data from Exercise 1, we get a P-value of 0.0041 when testing the claim that s 6 0.04000g. a. What should we conclude about the null hypothesis? b. What should we conclude about the original claim? c. What do these results suggest about the new minting process? 8-4 Basic Skills and Concepts 422 CHAPTER 8 Hypothesis Testing
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