Can a human swim faster in water or in syrup? It is unknown whether the increase in the friction of the body moving through the syrup (slowing the swimmer down) is compensated by the increased power of each stroke (speeding the swimmer up). Finally, an experiment was done in which researchers filled one pool with water mixed with syrup (guar gum) and another pool with normal water (Gettelfinger and Cussler 2004). They had 18 swimmers swim laps in both pools in random order. The data are presented as the relative speed of each swimmer in syrup (speed in the syrup pool divided by his or her speed in the water pool). If the syrup has no effect on swimming speed, then relative swim speed should have a mean of 1. The data, which are approximately normally distributed, are as follows:

Σ(Y)=18.21, Σ(Y²) =18.4529.

a. Draw a graph showing the frequency distribution. Why is this a good idea? Does the graph suggest that swim speed increased, decreased, or stayed about the same in syrup?

b. Test the hypothesis that relative swim speed in syrup has a mean of 1.

c. How uncertain are we about true relative swimming speed in syrup? Use the 99% confidence interval to find out.

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1.08,1.08, 0.94,0.94, 1.07,1.07, 1.04,1.04, 1.02.1.02, 1.01.1.01, 0.95,0.95, 1.02,1.02, 1.081.08 1.02,1.02, 1.01,1.01, 0.96,0.96, 1.04.1.04, 1.02.1.02, 1.02,1.02, 0.96,0.96, 0.98,0.98, 0.990.99