Although runners tend to slow with age, for a runner who was never all that fast, the loss in speed can be small. The table contains speeds in kilometers per hour for two ten kilometer runs, one in 2009 and one in 2014. Speeds were recorded for each kilometer along the same route. If the 95% confidence intervals for each run "overlap" the mean for the run, then the difference in speeds is not significant. If the 95% confidence intervals for each year do not overlap each other at all, then the speed difference is significant. If the 95% confidence intervals overlap but not enough to include the other mean, then the difference may nor may not be significant. For each data set, the 2009 and the 2014, calculate the following:
Calculate the sample size n.
Calculate the zeroth quartile.
Calculate the first quartile.
Calculate the second quartile.
Calculate the third quartile.
Calculate the fourth quartile.
Calculate the range.
Calculate the mode.
Calculate the median.
Calculate the sample mean x.
Calculate the sample standard deviation sx.
Calculate the standard error of the sample mean x
Calculate tcritical for a confidence level c of 95%
Calculate the margin of error E for the sample mean x.
Write out the 95% confidence interval for the population mean μ speed of sound.
p( __ < μ < __ ) = 0.95
If you can, sketch out on a piece of paper the two confidence intervals, one for 2009 and one for 2014. Do the intervals overlap the mean for the other data? This would mean there is no significant difference in the mean speeds between 2009 and 2014.
If the intervals do not overlap the other mean, then are the intervals completely non-overlapping? This would mean there IS a significant difference in the mean speeds between 2009 and 2014.
If neither of the above two conditions is true, then the difference may or may not be significant. Determining whether the difference is significant will require a different statistical analysis.