6. Sociology: Job Changes A sociologist is interested in the relation between x 5 number of job changes and y 5 annual salary (in thousands of dollars)

for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information:

x (Number of job changes) 4 7 5 6 1 5 9 10 10 3 y (Salary in $1000) 33 37 34 32 32 38 43 37 40 33

©x 5 60; ©y 5 359; ©x2 5 442; ©y2 5 13,013; ©xy 5 2231

(a) Draw a scatter diagram for the data.

(b) Find x, y,

b, and the equation of the least-squares line. Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coefficient r and the coefficient of determination.

What percentage of variation in y is explained by the least-squares model?

(d) Test the claim that the population correlation coefficient r is positive at the 5% level of significance.

(e) If someone had x 5 2 job changes, what does the least-squares line predict for y, the annual salary?

(f) Verify that Se < 2.56.

(g) Find a 90% confidence interval for the annual salary of an individual with x 5 2 job changes.

(h) Test the claim that the slope b of the population least-squares line is positive at the 5% level of significance.

(i) Find a 90% confidence interval for b and interpret its meaning.