What is level of significance? I am always confused with meaning of level of significance especially when my null hypothesis got accepted at 5% level and rejected at 1% level, how it could be possible that investigators would have two different decisions by merely changing levels of significance ?
Can anybody please explain procedures for selecting correct level of significance?

The standard significance level is $5\%$, which indicates a $5\%$ chance of concluding that a difference exists when there actually is no difference at all. Thus, lower levels of significance reduce the risk of an incorrect conclusion.
The $P$-value on the other hand indicates the probability of obtaining such an extreme value, assuming the null hypothesis is true. Thus, we can reject the null hypothesis (that there is no difference) and accept the alternate hypothesis (that there is actually a difference) when the $P$-value is less than the level of significance.
However, this $5\%$ level is not necessarily set and the statistician must indicate the level of significance. For example, the long-sought Higgs Boson particle has been labeled with $5\sigma$ with a $P$-value of $3\cdot10^{-7}$. This indicates the probability that the physicists would collect data this extreme if the particle did not exist. As you can see, the significance level for testing the null hypothesis can be widely flexible. 
