How can I calculate the p-value (statistical significance) if my hypothesis asks for specific mean values?

How can I calculate the p-value (statistical significance) if my hypothesis asks for specific mean values?

(Cross-Post with no answer yet: ANOVA test mean against predefined constant)

I suppose this can be somehow calculated using ANOVA, but I could only find examples where the hypothesis states that all means are the same.

I.e. I have four groups, and my hypothesis states that the means will be:

x1=1

x2=2

x3=3

x4=4

x2=2

x3=3

x4=4

Example:

Example:

Suppose the following (simplified) example:

I collect data by asking people on the street to order fruits according to their preference. There are four fruits (groups) to order: apple, banana, coconut, pear

So if participant P1 likes apples A the most, followed by coconut C, then pear P and bananas B as least preferred, I note the following data (position in the ordered list):

P1: A=1, B=4, C=2, P=3

P2: A=2, B=4, C=3, P=1

A | B | C | P

----------------------------------------

1 | 4 | 2 | 3

2 | 4 | 3 | 1

... and a lot more data

----------------------------------------

1 | 4 | 2 | 3

2 | 4 | 3 | 1

... and a lot more data

xA = 1

xB = 2

xC = 3

xP = 4

xB = 2

xC = 3

xP = 4

Thanks!