Many runners believe that listening to music while running enhances their performance. A recent study wanted to determine if this were true. Eleven triathletes were chosen at random. They recorded time to exhaustion while running on a treadmill at a speed determined to be their peak running velocity. Each was recorded on two separate days, one while listening to music and one without music. The data is provided in the following table (time in seconds): Runner With Music Without Music 1 535 467 2 533 446 3 527 482 4 524 573 5 431 562 6 498 592 7 555 473 8 396 496 9 539 552 10 542 500 11 523 524 1) Using an alpha level of 0.05, test the relevant hypotheses that there was and improvement in performance when listening to music. Due to a small sample size I assume that the distribution of differences for the population of triathletes is normal du 2) Construct and interpret a 95% confidence interval for the difference in mean time to exhaustion. 68+87+45-49-131-94+82-100-13+42-1/11=5.292 Sq root of (68-5.292)^2+(87-5.292)^2+(-1-5.292)^2/10=78.0395 -.0247 p value > a fail to reject hypothesis 3) Comment on any issues you might have with this study. There does not seem to be evidence that would be convincing that mean time exhaustion is greater when the run listening to music