EXCEL MINITAB TI-84 PLUS TECHNOLOGY Technology 463 Extended solutions are given in the technology manuals that accompany this text. Technical instruction is provided for Minitab, Excel, and the TI-84 Plus. Tails over Heads 1. Use technology to perform a one-sample z@test to test the hypothesis that the proportion of coins found lying heads up is 0.5. Use a = 0.01. Use Casey’s data as your sample and write your conclusion as a sentence. 2. Do Casey’s data differ significantly from chance? If so, what might be the reason? 3. In the simulation shown above, what percent of the trials had heads less than or equal to the number of heads in Casey’s data? Use technology to repeat the simulation. Are your results comparable? In Exercises 4 and 5, use technology to perform a two-sample t-test to determine whether there is a difference in the mint dates and in the values of coins found on a street from 1985 through 1996 for the two mint locations. Write your conclusion as a sentence. Use a = 0.05. 4. Mint dates of coins (years) Philadelphia: x1 = 1984.8 s1 = 8.6 Denver: x2 = 1983.4 s2 = 8.4 Assume population variances are equal. 5. Value of coins (dollars) Philadelphia: x1 = $0.034 s1 = $0.054 Denver: x2 = $0.033 s2 = $0.052 Assume population variances are not equal. EXERCISES In the article “Tails over Heads” in the Washington Post (Oct. 13, 1996), journalist William Casey describes one of his hobbies—keeping track of every coin he finds on the street! From January 1, 1985, until the article was written, Casey found 11,902 coins. As each coin is found, Casey records the time, date, location, value, mint location, and whether the coin is lying heads up or tails up. In the article, Casey notes that 6130 coins were found tails up and 5772 were found heads up. Of the 11,902 coins found, 43 were minted in San Francisco, 7133 were minted in Philadelphia, and 4726 were minted in Denver. A simulation of Casey’s experiment can be done in Minitab as shown below. A frequency histogram of one simulation’s results is shown at the right. 10 20 30 40 50 60 70 80 x f 5770 6130 6110 6090 6070 6050 6030 6010 5990 5970 5950 5930 5910 5890 5870 5850 5830 5810 5790 Number of heads Frequency Coin Toss Simulation Sample From Columns... Bernoulli... Geometric... Chi-Square... Normal... Multivariate Normal... F... t... Uniform... Binomial... MINITAB Number of rows of data to generate: 500 Store in column(s): C1 Number of trials: 11902 Event probability: .5
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