Researchers studied ergometer (rowing machine) times for international male competitors in the 2007 World Junior Rowing Championships.

Question:

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.