Goodness-of-Fit Test Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER continued TI-83, 84 Plus Calculator TI-83>84 calculators require expected frequencies. Expected proportions cannot be used. 1. Enter the observed values in a list (L1) and expected frequencies in a separate list (L2). 2. Press K, then select TESTS in the top menu. 3. Select X2 GOF-Test in the menu and press [. 4. Enter the list names for the observed and expected frequencies. For df enter the degrees of freedom, which is 1 less than the number of categories. 5. Select Calculate and press [. TIP: TI-83 calculators require the program X2GOF, which is available at TriolaStats.com. R R commands: Equal expected frequencies: chisq.test1x2 Unequal expected frequencies: chisq.test1x, p=y2 where x are the observed values and y are the expected proportions. A complete list of R statistical commands is available at TriolaStats.com Excel XLSTAT Add-In 1. Click on the XLSTAT tab in the Ribbon and then click Parametric tests. 2. Select Multinomial goodness of fit test from the dropdown menu. 3. Under Data format, select Frequencies or Proportions for the expected data format. 4. In the Frequencies box enter the range of cells containing the observed frequencies. In the Expected frequencies/ proportions box enter the range of cells containing the expected data. 5. Check the Chi-square test box. 6. Enter a significance level and click OK. The test statistic is labeled Chi-Square (Observed Value). Excel 1. Click Insert Function ƒx, select the category Statistical, and select the function CHISQ.TEST. 2. For Actual_range enter the cell range for observed frequencies. For Expected_range enter the cell range for the expected frequencies. 3. Click OK for the P-value. 586 CHAPTER 11 Goodness-of-Fit and Contingency Tables Statistical Literacy and Critical Thinking 1. Cybersecurity The table below lists the frequency of leading digits of Internet traffic interarrival times for a computer, along with the percentages of each leading digit expected with Benford’s law. a. Identify the general notation used for observed and expected values. b. Identify the observed and expected values for the leading digit of 2. c. Use the results from part (b) to find the contribution to the x2 test statistic from the category representing the leading digit of 2. Leading Digit 1 2 3 4 5 6 7 8 9 Benford’s Law 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% Leading Digits of Interarrival Traffic Times 76 62 29 33 19 27 28 21 22 2. Cybersecurity When using the data from Exercise 1 to test for goodness-of-fit with the distribution described by Benford’s law, identify the null and alternative hypotheses. 11-1 Basic Skills and Concepts
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