Introduction to Hypothesis Testing

BHS 220 Module 4 - Case-INTRODUCTION TO HYPOTHESIS TESTING
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Probability
Probability is an integral component of statistics, with the frequency of an outcome, whereby determining the relative frequency of a population (Cook et al., 2004). When there is no prior knowledge about the possible outcomes of an event, then there is an assumption that all outcomes have an equal chance of occurring. The outcomes are mutually exclusive while the events are independent. Probabilities representing the possible outcomes help to demonstrate probability distributions, with the shape of the probability distribution curve influenced by the mathematical distribution (Cook et al., 2004). In the standard normal distribution, it is assumed that the population is truly homogenous when calculating for the Z-test. Furthermore, the underlying distribution is assumed to be normal, with sample distribution being homogenous (Michelson & Schofield, 2002).
Probability relates to the likelihood of an event happening, where a value of 0 indicates that there are no chances fro the event to occur, while 1 indicates that there is certainty that the event will definitely occur. The history of probability was started with the need to utilize computing methods to improve chances of winning during gambling games in France during the 17th century. As such Blaise Pascal and Pierre Fermat led to formulation of the classical approach in probability, which takes into outcome likely outcome of a game (Sox et al., 2013). The frequency method was another early approach that was consistent with the classical approach.
Theory of probability
The theory of probability states that one cannot realistically know about the probability, although the measure is an objective quantity. In other words the relative frequency of an event occurring determines the probability, depending on the number of times that the event occurred compared to possible times in which the event could occur (Norman, G., and Streiner, 2008). Nonetheless, there are various theories of probability which deal with probability, with the Bayesian probability being the most common and Markov models to an extent. It follows that when there are two events A and B then:
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Advantages of the Bayesian approach
When using the Bayesian approach it is possible to use previous results and add the new information into a model. At the same time, when relying on a model, the approach is suited to deal with complex systems, as there is no need for model modification in comparison to frequentist inference (Sox et al., 2013). The data attributed to the Bayesian approach is fixed, while the parameters are random, and the conditionality approach in Bayesian inference facilitates estimation. In any case the Bayesian approach is a probability model that can be useful in hypothesis testing. Given that the approach takes into account two events or more, it is helpful in facilitating...