Pension benefits. The defined-benefit (DB) pension plan guarantees a certain income to employees when they retire. The defined-contribution (DC) plan specifies that a regular contribution will be made to an investment account, and upon retirement, the employee will receive the income from the investment. The DBhas been the traditional plan but in recent years there has been a shift toward DC. One study examined the change in the proportion of DC-covered employees in 40 different industries.14 The researchers who conducted the study used multiple regression methods to examine the effects of various explanatory variables on the change in the proportion of individuals covered by DC plans over a 20-year period. One set of variables were classified as “supply-side” factors that relate to changes in firm characteristics.

One of these focused on quantifying shorter-term employment relationships using the change in the proportion of workers with fewer than 5 years with the company. The researchers called this variable P5. Variables such as age, gender, and region of residence were included in the model to control for these factors. A total of 30 variables were included.

(a) In a model to predict the change in the proportion ofDCplans, the regression coefficient for P5 is 0.625 with a standard error of 0.189. Construct the t statistic for testing the null hypothesis that the coefficient for P5 is zero. Carry out the test and summarize the result.

(b) Give a 95% confidence interval for the coefficient for P5.

From your calculations in part

(a) of this exercise, would you expect the interval to include zero? Explain your answer.