I want to know if my sample size is adequate I am trying to critique a research paper and I do not remember how to calculate statistics.  It was a few years ago.  The sample size is 40.  I'd also like to discuss the hypothesis; I'm not sure it is correct.
I am going to write out the abstract:

This quasi-experimental and cross-sectional study was carried out to determine the efficacy of back massage, a nursing intervention, on the process of acute fatigue developing due to chemotherapy and on the anxiety level emerging in cancer patients receiving chemotherapy during this process.   The study was conducted on 40 patients.  To collect data, ... [reliability and validity seemed adequate].
In our study it was determined that mean anxiety scores decreased in the intervention group patients after chemotherapy.  The level of fatigue in the intervention group decreased statistically significantly on the next day after chemotherapy (p=.020; effect size=0.84). At the same time, the mean anxiety scores of the patients in the intervention group decreased right after the massage was provided during chemotherapy (p=.109; effect size=0.37) and after chemotherapy.
In line with our study findings, it can be said that back massage given during chemotherapy affects anxiety and fatigue suffered during the chemotherapy process and that it significantly reduces state anxiety and acute fatigue.

 A: Looking ahead, it seems that a sample size of $n = 40$ may be sufficient
in this study, but without more-specific information it is not possible
to say four sure.
It is not possible to do a power computation for detecting a change in binomial $p$ in testing $H_0: p = p_0$ against $H_a: p < p_0$ without knowing both the specific null value $p_0$ and the size of the effect
to be detected. 
In the anxiety test you mention one might suppose
researchers wanted to detect a decrease of $0.35,$ but for a precise power
computation, we would need to know $p_0$ as well.
If $p_0 = .5$ and the target value to be detected is $0.5 - 0.35 = 0.15,$
then in order to have power $0.95$ (probability of detecting the change) in a test at the 5% level, then the required sample size is $n = 17,$ as shown by the Minitab output below. So $n = 40$ subjects should have been enough to detect a change of $0.35.$
Power and Sample Size 

Test for One Proportion

Testing p = 0.5 (versus < 0.5)
α = 0.05


              Sample  Target
Comparison p    Size   Power  Actual Power
        0.15      14    0.90      0.913764
        0.15      17    0.95      0.958912


In another scenario, if $p_0 = 0.8, n = 40,$ and $\alpha = 0.05,$  the following output shows that target values below about 
$p = 0.6$ would be detected with power $0.9.$
Power and Sample Size 

Test for One Proportion

Testing p = 0.8 (versus < 0.8)
α = 0.05

Sample
  Size  Power  Comparison p
    40   0.90      0.596562
    40   0.95      0.567110

