Introduction to Hypothesis Testing

Introduction to Hypothesis Testing
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Introduction to Hypothesis Testing
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 the degree or measure of how likely an event is. An event in this case is the chances of an outcome of an experiment. Probability emerged during the mid-seventeenth century; the term probability comes from the word ‘probable’ meaning approval. Gerolamo Cardano demonstrated the effectiveness of describing odds of an event as the ratio of favorable chance to unfavorable chance. Therefore implying that the probability of something happening is given by the ration of favorable outcomes of the total number of possible outcomes. This is the first breakthrough to probability. Since then, other researchers have constantly improved and contributed to probability over the years. The introduction of theories from people like Andrey Markov for Markov Chains, helped in the understanding of stochastic processes.
The theory of probability is a demonstration of probabilistic concepts in recognized terms. Thus, manipulation of these formal terms by use of mathematics rules and logic, resulting to translation of the result back to the problem domain. The Kolmogorov formulation and the Cox formulation have been successfully been useful in formalizing probability.
To find out probability of an event happening, one needs to find the number of ways it is likely to happen and then divide by the total number of outcomes. Probability is always between number 1 and 0 and it is just a guide on what is to happen.
Advantages of probability includes fairness in contests when selecting one individual from a long list of people or an event. An individual puts names in a container and each individual is to pick one name thus creating fairness. In addition, another advantage is sampling errors calculated.
Disadvantage includes high possibility of flaws to the randomness model has other people might easily cheat of interfere with the process. For example, someone might add illegal forms or duplicate the forms thus increasing the chances of one individual his winning. The process is also time consuming and expensive.
2 Identify and discuss the two major categories of probability interpretations, whose adherents possess conflicting views about the fundamen...