Understanding the use of the standard error of differences between two means (SEDM)

#1
Hello everyone,

I am currently learning statistics using Van Emden's "Statistics for terrified biologists". I am trying to solve some exercices that the book offers you.

One of the questions (1b) in the "Spare-time activities" section asks to find out if a mean value of 240 coming from the yield of 10 strawberry plants is statistically significant in comparison with a set of 10 mean yields of 10 strawberry plants each (values: 239, 176, 235, 217, 234, 216, 318, 190, 181, and 225).

I understand that when you calculate the variance of the last 10 values, you get the standard error of the mean (SEM), in this case 40.41 . I would think that you then check if the new value of 240 is within 2σ of the mean of the 10 mean yields (223.1), which it is. But the solution in the book uses the SEDM. I do not understand why it is relevant to use the SEDM here and not the SEM, since we are not comparing means of a sample buth rather checking if a newly acquired mean fits in a sampling distribution.

Here is the exercise and solution (1b) as give in the book for clarification, since English is not my first language.
EmdenQ1S.JPG

Thanks in advance,

CaptBluetooth