Scenario 3Runner Music No Music153546825314493528482524571543356249659275554718399499537552105425001152152412534555Do the data provide convincing evidence that the meantime to exhaustion for experienced triathletes isdifferent when they run while listening to motivationalmusic? Test the relevant hypotheses using asignificance level of 0.1.Suggestion: write out every step in the hypothesistest.6. Scenario 3Some runners believe that listening to music whilerunning enhances their performance. Some say musichinders their performance. The authors of a paperwondered if this is true for experienced runners. Theyrecorded time to exhaustion for these triathletes whilerunning on a treadmill at a speed determined to benear their peak running velocity. The time to exhaustionwas recorded for each participant on two differentdays. On one day, each participant ran while listeningto music that the runner selected as motivational. On adifferent day, each participant ran with no musicplaying. For purposes of this exercise, assume that it isreasonable to regard these triathletes as representativeof the population of experienced triathletes. Onlysummary quantities were given in the paper, but thedata in the table below are consistent with the meansand standard deviations given in the paper.

Applying the paired 't' test: sample size,n= 12 mean (d̄) =Σd/n =-90/12 = -7.5 standard deviation, Sd=√(d-d̄)2)/n-1) = √60215/(12-1) = 73.9871 The null and alternative hypothesis Ho : μd = 0 Ha : μd > 0 Test statistic = (d̄ -μd)/(Sd/√n) = (-7.5-0)/( 73.9871/√12) = -0.3512 degree of freedom (df) = n-1 = 12-1 = 11 significance level α = 0.1 For a right tailed test,tcritical = tα/2 ,df = 1.3634 (from t distribution table) Since test statistic(t) < tcritical , we fail to reject the null hypothesis. The result is not significant at the 0.1 significance level. Conclusion: At the 0.1 significance level we conclude that the data do not provide convincing evidence that the mean time to exhaustion for experienced triathletes is greater when they run while listening to motivational music