Chapter 12, Problem 70H

Table 12.22 gives the gold medal times for every other Summer Olympics for the women’s 100-meter freestyle

(swimming).

Year	Time (seconds)
1912	82.2
1924	72.4
1932	66.8
1952	66.8
1960	61.2
1968	60.0
1976	55.65
1984	55.92
1992	54.64
2000	53.8
2008	53.1

Table 12.22a. Decide which variable should be the independent variable and which should be the dependent variable.

b. Draw a scatter plot of the data.

c. Does it appear from inspection that there is a relationship between the variables? Why or why not?

d. Calculate the least squares line. Put the equation in the form of: $\hat{y}\text{=}a+bx$.

e. Find the correlation coefficient. Is the decrease in times significant?

f. Find the estimated gold medal time for 1932. Find the estimated time for 1984.

g. Why are the answers from part f different from the chart values?

h. Does it appear that a line is the best way to fit the data? Why or why not?

i. Use the least-squares line to estimate the gold medal time for the next Summer Olympics. Do you think that your

answer is reasonable? Why or why not?