Researchers studied ergometer (rowing machine) times for international male competitors in the 2007 World Junior Rowing Championships. They found that the mean time to row 2000 meters on an ergometer for the population of international sculls competitors was 387 seconds (?Does 2000-m Rowing Ergometer Performance Time Correlate with Final Rankings at the World Junior Rowing Championship? A Case Study of 398 Elite Junior Rowers,? Journal of Sports Sciences [2009]: 361?366). A related research team studied a sample of 24 junior male sculls rowers from only the United States in 2013?2014 and reported summary statistics for their 2000-meter ergometer times (?Correlates of Performance at the U.S. Rowing Youth National Championships: A Case Study of 152 Junior Rowers,? The Sport Journal, March 3, 2014). Data for a representative sample of 24 rowers that are consistent with summary statistics given in the paper are shown in the accompanying table.

a. Use the Shiny app output at the bottom of the page to carry out a randomization test of the hypothesis that the population mean 2000-meter ergometer time for U.S. junior male sculls rowers differs from the 2007 international standard of 387 seconds. Use a significance level of 0.05.

b. Based on the result of the hypothesis test, does it seem that the U.S. junior male sculls rowers have ?caught up,? on average, with the international championship rowers from 2007? Explain.

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Time Time Rower ID (seconds) Rower ID (seconds) 391 13 404 389 14 399 3 386 15 390 396 16 395 5 395 17 392 409 18 401 406 19 381 8. 402 20 392 9. 393 21 376 10 392 22 400 11 382 23 388 12 401 24 402 1. Randomization Distribution 100 50 382 390 392 386 388 394 304 Sample Mean Observed Sample Mean Simulation Standard Error Two-Tailed P-value Number of Values in Tail Number of Simulated Samples 394.250 1.654 1000 0.000 Frequency