I am a 63-year-old woman who was a nanny for a family for several months last year.They paid me in cash, which means they did NOT consider me an employee and did not withhold FICA taxes. When I apply for my Social Security benefits (possibly soon), am I correct in deducing that I cannot list this family as people for whom I have worked? (Questions 19-20 on the Application For Retirement Insurance Benefits, Form SSA-1-BK)
There are a numerous factors involved in determining whether or not an employer-employee relationship exists (https://www.ssa.gov/pubs/EN-05-10021.pdf), so I can't say for sure whether or not the family you worked for should have considered you as an employee and withheld Social Security taxes from your pay. In any case, it certainly sounds like the pay that you received was earned income, so if you did not receive a W-2 form you may be required to report this income as self-employment earnings. For more information, refer to IRS's website: https://www.irs.gov/publications/p334/ch10.html.
The intent of the question that you refer to on Social Security's application form is to make sure that all of your recent earnings are posted to your earnings record so that your benefit rate can be properly computed. You would only want to list the family that you worked for as an employer if you believe that they were required by law to withhold Social Security taxes from your pay.