Marathon start-up years When we considered the Boston Marathon in Exercise 37, we were unable to check the Nearly Normal Condition. Heres a histogram of the differences: Those three large differences are the first three years of wheelchair competition: 1977, 1978, and 1979. Often the start-up years of new events are different; later on, more athletes train and compete. If we omit those three years, the summary statistics change as follows: Summary of wheelchrF - runM N = 31 Mean = -12.794 SD = 18.64 a) Comment on the assumptions and conditions. b) Assuming that these times are representative of such races, construct and interpret a 95% confidence interval for the mean difference in finishing time. c) Would a hypothesis test at a = 0.05 reject the null hypothesis of no difference? What conclusion would you draw?

STAT-5615: Statistics in Research I Lecture 11 ANOVA Ott & Longnecker Ch 8 Dr. Christian Lucero Virginia Tech Fall 2016 ANOVA - Analysis of Variance Despite it’s name, the Analysis of Variance is a very useful method that can be used for many di▯erent statistical analyses. The most important way that we will use it is to compare the means of many independent samples simultaneously. Main Ideas Suppose we have multiple populations that we want to compare a possible null is H 0 m 1 = m 2= ▯▯▯ = mt where t is the total number of population groups. The alternative is that at least one mean di▯ers, i.e. H A m m 6= mn for some m