Hypothesis Testing

Hypothesis Testing
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1] Discuss probability. What is its history? What is the theory of probability? How is it calculated? What are the advantages and disadvantages of using this technique?
Probability is concerned with understanding how chance affects certain outcomes of a random phenomenon (Michelson & Schofield, 2002). Probability and statistics are closely related, and probability predicts the likelihood that an event is likely to occur, but probability is a subset on the subject matter of statistics. Typically the probability that an event will occur is dependent on the likelihood that the event would occur in a number of ways as well as the final outcomes. Even though, probability has an element of uncertainty, when there are no known chances of occurrences, each event has equal chance among the outcomes. At the same time, probability distributions provide a clear picture of the population distribution. The normal distribution is then used in hypothesis testing as it may represent the probability distribution curve. Estimating the P value extends from statistical hypothesis testing, with the P value used to calculate probabilities (McDonald, 2009).
Since the likelihood that all events in will occur, is one the likelihood of one event occurring is between 0 and 1. With 0 indicating that an event cannot occur while 1 indicates that there is certainty that the event (s) will occur. The history of probability is closely tied to finding clues on how to win the game of chances. As such, improving the odds of winning in gambling is well grounded in the probability. The theory of probability focuses on the relative frequency and total number of outcomes determine probability. As such, Bayesian analysis is one of the most common approaches to the theory of probability. In probability testing, setting the level of significance depending on the test to determine the probability of rejecting or not rejecting the null hypothesis (Davis & Mukamal, 2002).
There are various advantages of Bayesian probability the technique allows use of subjectivist interpretations as well as comparison of various hypotheses. At the same time, the approach allows one to use various models, while also integrating new data to facilitate computation of complex systems. Since Bayesian methods integrate prior information, they facilitate the decision making and hypothesis testing. As such, both past information and new observations are sued to make inferences. Nonetheless, the inferences also depended on the data. In any case, it follows the likelihood principle unlike classical inference.
However, there are also disadvantages of Bayesian analysis, with the approach ignoring the process of choosing a prior. Since the subjective prior beliefs influence the decision-making process one needs to understand how to interpret Bayesian inferences. The approach might generate misleading results if one relies on Bayesian inferences without having good ability to interpret the prior. At other times, the priors have too much influence on the posterior distributions. Besides re...