Does low significance prove my hypothesis wrong? I have no idea about statistical testing yet I am doing a research project on a sample size of 40; it is a correlational study using Pearson's r (SPSS).  My results indicate Pearson's correlations (2-tailed p) of  
-.264 (.100): self efficacy
-.113 (.489): social support
-.172 (.290): happiness

My hypothesis states that these variables will be negatively correlated with stress
but it doesn't say significantly, so I think that my hypothesis is proved as it's negatively correlated.  Am I thinking something which is impossible or wrong or stupid or am I right?
In simple words, I cannot state that my hypothesis is proved, can I? 
 A: Your null hypothesis is that self-efficacy, social support, and happiness are uncorrelated with stress. The negative signs on the first number indicate that the direction of the first order trend is negative, but the p-values in parentheses show that there is not sufficient evidence to conclude that there is an association between these variables.
A: I think that you are missing the distinction between parameters and statistics.  
There is a Pearson correlation of the entire population including subjects that you have not measured.  This correlation is a parameter (refers to the population or the theoretical value for future observations).  The parameter is something that theoretically exists: if you had infinite resources you could calculate it exactly, but since you don't have infinite resources you do not know the value of the parameter and therefore need to make inference about it.
You calculated a correlation for the sample of subjects that you actually observed, this correlation is a statistic (a measured value from the sample).  
A meaningful null hypothesis is about an unknown parameter value, so while you can say that the observed statistics are not 0, the fact that you are not seeing significant p-values means that you cannot rule out the possibility of the population correlation (parameter) being 0.
Focusing on only the statistic computed from past observations and ignoring inference about the parameter is like playing Russian Roulette where someone loads a live bullet into 1 chamber (of 6) of a relvover and spins the cylinder to randomize the bullets location.  They then pull the trigger 3 times and it clicks on an empty chamber each time.  They then hand the gun to you and expect you to hold it up to your head and pull the trigger stating that 0% of the data so far resulted in a bullet firing so you are perfectly safe.
A: You may not have a sufficient sample size to be able to detect an effect. Given that the coefficients are in the right direction, do a post hoc power analysis to see what kind of sample size you need, and collect more data, if possible.
