In this thesis we’ve illustrated the use of the bootstrap method for testing statistical hypotheses and constructing confidence intervals for parameters of various models. Even though there is a great number of theoretical results derived for both of these methods of statistical inference, often the assumptions under which those results work are not met in practice. This is the reason why we need to resort to approximate methods. The main point of this method is to use the available sample to estimate certain parameters and then use those estimates as if they were the real parameter values. Intuitively, all the information about the population of interest is contained in the sample, so basically we treat the sample as the population. By simulating samples from the fitted distribution we get an insight on the shape of sampling distribution of statistic of interest. Although this method is only approximate, we’ve shown through numerous examples how efficient it can be and that it results in satisfying and quick estimates. We’ve also demonstrated how each of the methods we presented can be improved so that they give adjusted and even more precise results. We’ve developed various methods that work surprisingly well even when no assumptions are being made on the distribution of the sample values. Certainly the results are even more accurate when we have a parametric model available. Every method that we’ve presented was accompanied by an example illustrating the use of the method. In the examples we used computer simulation to help us compute complicated expressions (for instance, some complicated probabilities) which are used in the methods.