Supplementary Exercise 10.27 of IPS7e
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For 40 children born in an Egyptian village, measurements of
  - birth weight,
  - monthly income (of the family).

Both variables could be viewed as response variables, with the 
interest being in whether an association exists between them. 
Alternatively, one could try to predict birth weight from the
family income (which presumably corresponds to the period prior
to birth). The text gives information about the correlation coefficient,
corresponding to the former situation.

(a)+(b)+(c)  Based on the Pearson correlation coefficient of r=0.39 we 
can test the hypothesis H0: rho=0 (the population correlation, for a 
suitably defined population including births in the village under study 
and presumably also similar villages) as follows:

t = r*sqrt((n-2)/(1-r^2)) = 0.39*sqrt(38/(1-.39^2)) = 2.6109

which follows a t(38) distribution under H0. Table lookup, using df=30
as a conservative approximation, gives the critical values for a 
one-sided alternative Ha: rho>0 as

t=2.457 for P=0.01, and t=2.750 for P=0.005.

Therefore we conclude that 0.005<P<0.01, and the test statistic is
significant. The exactly calculated P-value in t(38) equals 0.0064.
There is (moderately strong) evidence to suggest that a positive 
(population) correlation exists between the two variables.


Minitab command and output to compute exact P-value in t(38):

---

 CDF -2.6109;
  T 38.

Student’s t distribution with 38 DF

      x  P( X = x )
-2.6109   0.0064271