Statistical model checking techniques have been shown to be effective for approximate model checking on large stochastic systems, where explicit representation of the state space is impractical. Importantly, these techniques ensure the validity of results with statistical guarantees on errors. There is an increasing interest in these classes of algorithms in computational systems biology since analysis using traditional model checking techniques does not scale well. In this context, we present two improvements to existing statistical model checking algorithms. Firstly, we construct an algorithm which removes the need of the user to define the indifference region, a critical parameter in previous sequential hypothesis testing algorithms. Secondly, we extend the algorithm to account for the case when there may be a limit on the computational resources that can be spent on verifying a property, i.e, if the original algorithm is not able to make a decision even after consuming the available amount of resources, we resort to a p-value based approach to make a decision. We demonstrate the improvements achieved by our algorithms in comparison to current algorithms first with a straightforward yet representative example, followed by a real biological model on cell fate of gustatory neurons with microRNAs.