We are interested in the total number of people who have never been married. From Example 1, we know the number of males, never married is 47,194,876. From summary table B12001 we have the number of females, never married is 41,142,530 with a margin of error of 84,363. Therefore, the estimated number of people who have never been married is 47,194,876 + 41,142,530 = 88,337,406.
To calculate the approximate standard error of this sum, we need the standard errors of the two estimates in the sum. We calculated the standard error for the number of males never married in Example 1 as 54,126. The standard error for the number of females never married
is calculated using the margin of error:
Using formula (2) for the approximate standard error of a sum or difference we have:
Caution: This method will underestimate or overestimate the standard error if the two estimates interact in either a positive or a negative way.
To calculate the lower and upper bounds of the 90 percent confidence interval around 88,337,406 using the standard error, simply multiply 74,563 by 1.645, then add and subtract the product from 88,337,406. Thus the 90 percent confidence interval for this estimate is
[88,337,406 - 1.645(74,563)] to [88,337,406 + 1.645(74,563)] or 88,460,062 to 88,214,750.