13-7 Runs Test for Randomness 691 INTERPRETATION We have sufficient evidence to reject randomness of the sequence of 50 mean global temperatures. If we simply examine the list of B’s and A’s, we see that the B’s are mostly in the beginning of the sequence and the A’s are mostly at the end, suggesting that over this period of 50 years, the mean global temperature is increasing. Also, because the significance level is a = 0.05 and we have a two-tailed test, the critical values are z = -1.96 and z = 1.96. The test statistic of z = -5.14 does fall within the critical region, so we again reject the null hypothesis of randomness. YOUR TURN. Do Exercise 9 “Testing for Randomness of Super Bowl Victories.” Runs Test for Randomness Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk 1. Determine the number of elements in the first category, the number of elements in the second category, and count the number of runs. 2. Click Analysis in the top menu. 3. Select Runs Test for Randomness from the dropdown menu. 4. Enter a significance level and the values for number of runs, number of elements in the first category (Element 1), and number of elements in the second category (Element 2). 5. Click Evaluate. StatCrunch Not available. Minitab Minitab will do a runs test with a sequence of numerical data only. The Minitab Student Laboratory Manual and Workbook provides additional information on how to circumvent this constraint. 1. Enter numerical data in column C1. 2. Click Stat in the top menu. 3. Select Nonparametrics from the dropdown menu and select Runs Test from the submenu. 4. Select column C1 under Variables. 5. Select to test above and below the mean or enter a desired value to be used. 6. Click OK. TI-83, 83 84 Plus Calculator 8 us Ca cu ato Not available. 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 Not available. Statistical Literacy and Critical Thinking In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat. RRRDRDRRRDRRRDDRDDRRDRRDRDR 1. Testing for Bias Can the runs test be used to show the proportion of Republicans is significantly greater than the proportion of Democrats? 13-7 Basic Skills and Concepts
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