Runs Test If we use a 0.05 significance level to test for randomness of the sequence

Testing for Bias The last 106 baseball seasons (as of this writing) ended with 62 World Series wins by American League teams and 44 wins by National League teams. Can the runs test be used to show that the American League is better because disproportionately more World Series contests are won by American League teams?

Notation Listed below are the most recent (as of this writing) winners of the NBA basketball championship game. The letter W denotes a winner from the Western Conference, and E denotes the winner is from the Eastern Conference. Use that sequence to identify the values of n 1 , n 2 , and G that would be used in the runs test for randomness. W W E E E E E W W W W W E W E W E W W W

Runs Test If we use a 0.05 significance level to test for randomness of the sequence given in Exercise 2, we conclude that there is not sufficient evidence to reject randomness. a. Rearrange the sequence so that randomness is rejected because the number of runs is very low. b. Rearrange the sequence so that randomness is rejected because the number of runs is very high.

Good Sample? Given a sequence of data, such as the one from Exercise 2, if we fail to reject the claim that the sequence appears to be random, does it follow that the sampling method is suitable for statistical methods? Explain.

Using the Runs Test for Randomness. In Exercises 510, use the runs test with a significance level of = 0.05 . (All data are listed in order by row.)Testing for Randomness of Presidential Election Winners The political parties of the winning candidates for a recent sequence of presidential elections are listed below. D denotes Democratic party and R denotes Republican party. Does it appear that we elect Democrat and Republican candidates in a sequence that is not random? R R D R D R R R R D D R R R D D D D D R R D D R R D R R R D D R R D

Using the Runs Test for Randomness. In Exercises 510, use the runs test with a significance level of = 0.05 . (All data are listed in order by row.)Odd and Even Digits in Pi A New York Times article about the calculation of decimal places of noted that mathematicians are pretty sure that the digits of are indistinguishable from any random sequence. Given below are the first 30 decimal places of . Test for randomness of odd (O) and even (E) digits. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9

Using the Runs Test for Randomness. In Exercises 510, use the runs test with a significance level of = 0.05 . (All data are listed in order by row.)psules, they were mixed, then capsules were selected to identify birth dates of men to be drafted first. The first 30 results are listed below. Test for randomness before and after the middle of the year, which is July 1. Sept. 14 Apr. 24 Dec. 30 Feb. 14 Oct. 18 Sept. 6 Oct. 26 Sept. 7 Nov. 22 Dec. 6 Aug 31 Dec. 7 July 8 Apr. 11 July 12 Dec. 29 Jan. 15 Sept. 26 Nov. 1 June 4 Aug. 10 June 26 July 24 Oct. 5 Feb. 19 Dec. 14 July 21 June 5 Mar. 2 Mar. 31

Using the Runs Test for Randomness. In Exercises 510, use the runs test with a significance level of = 0.05 . (All data are listed in order by row.)Newspapers Media experts claim that daily newspapers are declining because of Internet access. Listed below are the numbers of daily newspapers in the United States for a recent sequence of 20 years. Shown below those numbers are letters indicating whether the number is above (A) the median of 1514.5 or below (B) that median. Test for randomness of the numbers above and below the median. What do the results suggest? 1645 1642 1626 1611 1586 1570 1556 1548 1533 1520 1509 1489 1483 1480 1468 1457 1456 1457 1452 1437 A A A A A A A A A A B B B B B B B B B B

Runs Test with Large Samples. In Exercises 912, use the runs test with a significance level of = 0.05 . (All data are listed in order by row.)Testing for Randomness of Super Bowl Victories Listed below are the conference designations of teams that won the Super Bowl, where N denotes a team from the NFC and A denotes a team from the AFC. Do the results suggest that either conference is superior? N N A A A N A A A A A N A A A N N A N N N N N N N N N N N N N A A N A A N A A A A N A N N

Runs Test with Large Samples. In Exercises 912, use the runs test with a significance level of = 0.05 . (All data are listed in order by row.). Baseball World Series Victories Test the claim that the sequence of World Series wins by American League and National League teams is random. Given below are recent results (as of this writing), with American League and National League teams represented by A and N, respectively. A N A N N N A A A A N A A A A N A N N A A N N A A A A N A N N A A A A A N A N A N A N A A A A A A A N N A N A N N A A N N N A N A N A N A A A N N A A N N N N A A A N A N A N A A A N A N A A A N A N A A N A N A N

Runs Test with Large Samples. In Exercises 912, use the runs test with a significance level of = 0.05 . (All data are listed in order by row.). Stock Market: Testing for Randomness Above and Below the Median Listed below are the annual high values of the Dow Jones Industrial Average for a recent sequence of years (as of this writing). Test for randomness below and above the median. What does the result suggest about the stock market as an investment consideration? 969 995 943 985 969 842 951 1036 1052 892 882 1015 1000 908 898 1000 1024 1071 1287 1287 1553 1956 2722 2184 2791 3000 3169 3413 3794 3978 5216 6561 8259 9374 11568 11401 11350 10635 10454 10855 10941 12464 14198 13279 10580 11625

Runs Test with Large Samples. In Exercises 912, use the runs test with a significance level of = 0.05 . (All data are listed in order by row.)Global Warming Listed below are global mean temperatures ( C ) of the earth for 50 recent and consecutive years (based on data from the Goddard Institute for Space Studies). Test for randomness above and below the mean. What do the results suggest about global warming? 13.98 14.10 14.05 14.03 13.65 13.75 13.93 13.98 13.91 14.00 14.04 13.90 13.95 14.18 13.94 13.98 13.79 14.16 14.07 14.13 14.27 14.40 14.10 14.34 14.16 14.13 14.19 14.35 14.42 14.28 14.49 14.44 14.16 14.18 14.31 14.47 14.36 14.40 14.71 14.44 14.41 14.56 14.70 14.64 14.60 14.77 14.64 14.66 14.68 14.70

Finding Critical Values a. Using all of the elements A, A, A, B, B, B, B, B, B, list the 84 different possible sequences. b. Find the number of runs for each of the 84 sequences. c. Use the results from parts (a) and (b) to find your own critical values for G. d. Compare your results to those given in Table A10.