In 2004, researchers investigated the effect of? weed-killing herbicides on house pets. They examined 828 cats from homes where herbicides were used? regularly, diagnosing malignant lymphoma in 434 of them. Of the 120 cats from homes where no herbicides were? used, only 20 were found to have lymphoma. Find the standard error of the difference in the two proportions.
Let p^1 be the sample proportion of cats with lymphoma from homes where herbicides were used regularly and p^2be the sample proportion of cats with lymphoma from homes where no herbicides were used.
The standard error of the difference in the two proportions ?SE(p^1-p^2) = _______ (Round to four decimal places as needed.)