The stale claim that 40 percent of gun sales lack background checks - The Washington Post: The White House says the figure comes from a 1997 Institute of Justice report, written by Philip Cook of Duke University and Jens Ludwig of the University of Chicago. This study is based on data collected from a survey in 1994, just the Brady law requirements for background checks was coming into effect. (In fact, the questions concerned purchases in 1993 and 1994, while Brady law went into effect in early 1994.) In other words, this is a really old figure.
The data is available for researchers to explore at the Interuniversity consortium on political and social research (ICPSR) at the University of Michigan. Digging deeper, we find that the survey sample was just 251 people. (The survey was done by telephone, using a random-digit-dial method, with a response rate of 50 percent.) With this sample size, the 95 percent confidence interval will be plus or minus 6 percentage points.