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12.4

12.4. Runs Test for Randomness. Is this sequence random?. SSSSSSSSSSSWWWWWWW SWSWSWSWSWSWSWSWS SWSSWWSWWWSSWWSSSWWSSWWSS. Random Party?.

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12.4

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  1. 12.4 Runs Test for Randomness

  2. Is this sequence random? • SSSSSSSSSSSWWWWWWW • SWSWSWSWSWSWSWSWS • SWSSWWSWWWSSWWSSSWWSSWWSS

  3. Random Party? • For each successive presidential term from Teddy Roosevelt to George W. Bush (first term), the party affiliation controlling the White House is shown below, where R designates Republican and D designates Democrat. R RR D D R R D DDDD R D R R D R RR D D R • Historical Note: In cases in which the president died in office or resigned, the period during which the vice president finsished the term is not counted as a new term. • Test the sequence for randomness.

  4. Runs Test for Randomness • Sample Statistic – R = _______ R RR D D R R D DDDD R D R R D R RR D DR • Run is a sequence of… • How many runs do we have? R =

  5. Looking forward • Lack of randomness can be determined in two ways: • R is very _____ • SSSSSSSSSSSSWWWWWW • R is very _____ • SWSWSWSWSWSWSWSW • This piece of information will help us understand the hypotheses.

  6. The Test • Hypothesis • H0: • H1: • Find the critical values from table 10 in the back of the book • To use the table • n1= • n2= • In the table • c1 = this is our lower critical value • c2 = this is our upper critical value • Calculate the sample statistic: R = # of runs

  7. The decision process • Using R, c1, and c2we can determine whether or not the sequence is random. • If R<c1 we have … • If R> c2 we have … We _____________ null. • If c1 < R< c2 We _____________ null. • Draw a conclusion in context

  8. Assignment Day #1 • P 695 #1, 4-6, 11 • Assignment Day#2 • P. 695 #2, 7-10

  9. Political Party R RR D D R R D DDDD R D R R D R RR D DR RRR DD RR DDDDD R D RR D RRR DD R R = • n1= • n2= • Therefore, • c1 = • c2 = • Conclusion:

  10. What about this? • Silver iodide seeding of summer clouds was done over the Santa Catalina mountains of Arizona. Of great importance is the direction of the wind during the seeding process. A sequence of consecutive days gave the following compass readings for wind direction at seeding level at 5 A.M. (0 degrees represents true north). 170 160 175 288 195 140 124 219 197 184 183 224 33 49 175 74 103 166 27 302 61 72 93 172 Test this sequence for randomness.

  11. Runs Test About the Median • To do this test, we will simply find ______and then replace every number in the sequence with either _______. • A  ____________ • B ____________ • Once we have this new sequence the test is exactly the same as a Runs Test for Randomness.

  12. Median • TI Tip – Use 1-Var Stats on the TI to find the median. • The median of our data is ______. • Now our sequence will read… • n1= • n2= • Therefore, • c1 = • c2 = • Conclusion: R =

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