200 people respond that they earn between $45,000 and $49,999.99

20 people respond that they earn between $50,000 and $54,999.99

No-one in my survey earns more than this.

I also know (from other work) that there is a 10% chance that any person gets their income wrong by one band – i.e. it will be $5,000 too high or too low.

Am I justified in saying that the number of households in the $50,000-54,999.99 bracket is more than the 20 actually measured in my survey? Should this, in fact, be 29?

My logic is as follows: If 10% are getting the band wrong, then 20 of the 200 telling me they earn between $45,000 and $49,999.99 actually earn $5,000 more or less than this, and (assuming equal likelihood of getting the band too high or too low) 10 of these actually earn between $50,000 and $54,999.99. However, only 2 of the 20 stating that they earn between $50,000 and $54,999.99 will get the band wrong, and only 1 of these actually meant to select the $45,000-49,999.99 band. There should, therefore, be 20 + 10 - 1 households (a total of 29 households) in the $50,000 - $54,999.99 band.

Appreciate thoughts on whether this logic is correct? Is anyone able to point me to a book / paper where this issue is discussed (which must be quite common in survey work)?

Thanks.

Jake