This exercise is most easily completed with access to a computer and software; alternatively, you can use the formulas and do the computations with a calculator.

Mario insists that tall men receive higher wages than short men. To test his hypothesis, he collects height and hourly wage data from a random sample of ten men. Here are the data.

(Keep in mind they are entirely fictitious!)

a) Compute the mean and the standard deviation for each variable. Since this is a sample, divide by n – 1 when you calculate the variance.

b) Compute each man’s height Z-score and wage Z-score. (You can round off to one decimal place.)

c) Use graph paper to plot the data in a scatter plot. Put height on the X-axis and wages on the Y-axis. (Why?)

d) Compute the correlation coefficient using the average product-moment formula. Write a sentence or two of interpretation.

e) Compute R-squared, and write a sentence of interpretation.

f) Find the slope for the OLS regression line, and use the information provided to find the Y-intercept.

g) Write the regression equation. If Gus grew a centimeter, how much more would we expect him to earn per hour?
h) Do you agree with Mario? Why or why not?
(If you have access to a computer and statistical software, you can do this problem on the computer.)

Table 8.12. Height and wages: The data file Name Height (in meters) Hourly Wage (in dollars) Ahmed 1.7 7 Bertrand 1.6 6 Cheng 1.8 8 Darren 1.9 10 Eduardo 2.0 10 Fabrizio 2.0 12 Gus 1.5 6 Henri 1.8 7 Immanuel 1.7 8 Jaime 1.7 8