A study of the ability of individuals to walk in a straight line

(“Can We Really Walk Straight?” Amer. J. of Physical Anthro., 1992: 19–27) reported the accompanying data on cadence (strides per second) for a sample of randomly selected healthy men.

n 5 20 Xnew Xnew n 5 26

.95 .85 .92 .95 .93 .86 1.00 .92 .85 .81

.78 .93 .93 1.05 .93 1.06 1.06 .96 .81 .96 A normal probability plot gives substantial support to the assumption that the population distribution of cadence is approximately normal. A descriptive summary of the data from Minitab follows:

Variable N Mean Median TrMean StDev SEMean cadence 20 0.9255 0.9300 0.9261 0.0809 0.0181 Variable Min Max Q1 Q3 cadence 0.7800 1.0600 0.8525 0.9600

a. Calculate and interpret a 95% confidence interval for population mean cadence.

b. Calculate and interpret a 95% prediction interval for the cadence of a single individual randomly selected from this population.

c. Calculate an interval that includes at least 99% of the cadences in the population distribution using a confidence level of 95%.