Hypothesis Testing: Probability and the History of Probability

Introduction to Hypothesis Testing
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Probability
Probability and history of probability
Probability relates to the likelihood that an event will occur, and statistics focuses on frequency outcomes to determine probability. Events have an equal outcome if they are affected by the same factors, and the outcomes are typically mutually exclusive. The probability that all the events will occur is one, and hence ea the probability of one event occurring is below. As such, probability distributions are potentially useful to understand how the events a= occur and their probabilities. A normal standard curve is bell shaped and is neither skewed to the right or the left, and the Z test is calculated when there is stand and normal distribution, by taking into account the mean of a sample as well as the standard deviation (Michelson & Schofield, 2002). The history of wining is related to need to predict outcomes, was initially utilized to try and predict the chances that one would win in gambling during the 17th century. There were various approaches developed that all gave similar results in probability, with Blaisé Pascal and Pierre Fermat the earliest pioneers on the theory of probability. Hypothesis testing is one of the statistical inferences that may utilize probability, as it helps to assess the strength of evidence of the mean compared to the population (Davis & Mukamal, 2002)
Theory of probability
The theory of probability focuses on analyzing random phenomena, with outcomes depending on the occurrence of events (Norman, G., and Streiner, 2008). As such the theory of probability focuses on the relative frequency of events occurring and the frequency that the event will not occur. The Markov models and Bayes theorem are the common techniques that help in calculating the probability of an occurring or not occurring.
In calculating the conditional probability in the Bayes theorem, then one assumes that A and B are mutually exclusive events: it follows that
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Advantages and disadvantages of Theory of probability
The Bayeisan paradigm uses prior information, meaning that there is no need for further testing, and where possible one can calculate the credibility intervals similar to confidence interval. The Bayesian theorem facilitates hypothesis testing, allowing one decide on the best alternative to choose from, and is hence a useful tool in the decision making process. The Bayesian analysis also allows one to use other models in computing data including parametric and hierarchical models.
Nonetheless, there are drawbacks to the approach, and one cannot reliably tell the best way to select a prior, while there is a need for one to understand how Bayesian inferences are translated especially in complicated models. Additional, the p...