Fieller-Hinkley Ratio of Correlated Random Variables: Question On Applying Theory

#1
I am a senior in college writing a thesis analyzing and critiquing government income transfer programs, such as SNAP (food stamps).

Here is my issue. I am using data collected from the consumer expenditure survey, which will typically provide means, sample sizes, and standard errors. I am looking to see if the percentage of income households typically spend on food is statistically different from the percentage that is assumed by the US Goverment.

I have the following:

Mean Income= $8,082 with Standard Error of 132.08

Mean food expenditure= $3,073.42 with Standard Error 241.33

N=5280

Percent of Income Spent on Food = 3,073.42/8,802 = 38.03%

I would like to test whether this is statistically different from the government's assumption of 13.79%

I have calculated the ratio of means, but I am having trouble computing the ratio of standard errors, which I could use to perform a proportion hypothesis test. The two random variables are correlated with non-zero means, so I have determined that this is a Hinkley Ratio, but with the small amount of information I have available I am unsure how to proceed.

How do I use just this information to calculate a new standard error?

Thank you so much for any help provided, it is very appreciated.