Let's say I'm trying to tell whether my company's sales have had a downward trend over the last 10 years. Let's also say I have available to me the last 10 years of quarterly sales. If I run a bivariate regression with time as the independent variable and sales as the dependent variable, and if the regression coefficient for time is negative, do I need to examine the regression coefficient's t-statistic? I mean, aren't these data based on a census of my population of interest? If they're a census, why would I need statistical testing?
Basically I'm wondering how often my knee-jerk reaction to apply statistical testing has been wrong-headed.