one sample t-test --> nonparamatric equivalent?

Dear all,

this is my first post in this forum. I am working on my MBA thesis, and while creating my research research design/hypotheses,/questionnaire, I came across this question:

Is there a nonparametric equivalent to the one sample t-test?

My case: I gathered data on a question such as "At what level do people "A" exhibit skills compared to the average level exhibited by all people ("B")?"

It was coded on a 5-point Likert scale, anchored by 1 = extremely poor and 5 = excellent, with 3 = average. Since this is ordinal data, I prefer to use nonparametric tests (I know that in spite of this, parametric tests are sometimes used with such data).

It would be like asking:
1. "From your experience, how good are the CAR driving skills of people who also have a motor cycle driver's license compared to the average level of car driving skills for people who do NOT have a motor cycle license (but of course a car license)?"

1 extremely poor
2 below average
3 about average
4 above average
5 excellent

So I am asking for a comparison of the skills of "A" to the average. That is why I assumed I know the population mean because I defined it as the "average".

Unfortunately, I was not able to construct a decent pair of questions that ask for A and B separately, in which case I would have been able to use the Mann-Whitney test (right?).

Now I have a known population mean of 3 (set by 3 = average) and want to test whether the mean of my data about "A" is significantly different from the known population mean. For parametric data I would simply use a one sample t-test, and all would be well.

My question: Is there a nonparametric test to compare a one sample mean to a known mean?

I did not find anything on that. My current goofy "solution": I experimented with SPSS and used my one sample data and generated a dummy variable which I set at "3" for all respondents and then ran the Mann-Whitney test to compare means. Of course, the second sample has a mean of 3 with a SD of 0. The Mann-Whitney significance here is the same (very close) to when I run a one sample t-test with the data, so I guess the result is "correct".

I would highly appreciate any help or advice on this issue. Many thanks in advance,

Anatol
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