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# Recall the distracted driving study from example 22

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Recall the Distracted Driving study from Example 2.2. The reaction times (in milliseconds) for 16 students appear below and in the file driving.txt . Subject A B C D E F G H I J K L M N O P Cell 636 623 615 672 601 600 542 554 543 520 609 559 595 565 573 554 Control 604 556 540 522 459 544 513 470 556 531 599 537 619 536 554 467 (a) Analyze the differences in reaction times (cell phone minus control) for these subjects. Include numerical and graphical summaries of the distribution of differences. Comment on what this descriptive analysis reveals about whether talking on a cell phone tends to produce slower reaction times. (b) State the appropriate null and alternative hypotheses to be tested, in order to investigate the research question of whether talking on a cell phone tends to produce slower reaction times. (c) Conduct a simulation analysis of a randomization test for testing these hypotheses. Report the empirical p-value. Summarize the conclusion that you would draw from this analysis. (d) Comment on whether the conditions for applying a paired t -test and t -interval are satisfied for these data. (e) Conduct a paired t -test of these hypotheses. Report the value of the test statistic and the p-value. Indicate your test decision at the 0.05 and 0.01 significance levels, and summarize your conclusion. (f) Produce and interpret a 95% t -confidence interval for the population mean difference. Also produce and interpret a 95% prediction interval. Comment on how these two intervals compare. (g) Compare these analyses to that in Example 2.2. Which analysis would you recommend and why?

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Chance/Rossman, 2015 ISCAM III Example 4.3 314 Analysis (a) Analyzing the differences The sample mean difference in reaction times (cell minus control) is d x = 47.125 milliseconds, with a standard deviation of s d = 51.331 milliseconds. The dotplot reveals that most of the differences are positive, suggesting that subjects talking on a cell phone tend to take longer to react than subjects listening to a book-on-tape. (b) The null hypothesis says that the mean reaction time is the same among cell phone users as among book-on-tape listeners (H 0 : P cell P control = 0). The alternative says that the mean reaction time is larger among cell phone users than among book-on-tape listeners (H a : P cell P control > 0). (c) We can carry out the simulation easily with the applet or with R. Copying and pasting the data into the Matched Pairs applet with 1,000 repetitions we get the results shown here. Using R to carry out the simulation instead: MeanDiffs=0 for (i in 1:10000){ multiplier=sample(c(-1,1), 16, + replace=TRUE) RandomizedData=differences*multiplier MeanDiffs[i]=mean(RandomizedData) } From R: The empirical p-value is the proportion of these 10,000 repetitions in which the mean difference is 47.125 or more, because 47.125 is the value of the sample mean difference from the actual experimental data. None of the 10,000 repetitions produced such a large mean difference, so the empirical p-value is 0. The simulation therefore shows that we would almost never get a result as extreme as the actual experiment did, if there were really no difference between reactions to cell phone
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