a. In the context of this problem, describe a Type I error and its consequence. b. In the context of this problem, describe a Type II error and its consequence
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
A television manufacturer states that at least 90% of its TV sets will not need service during the first 3 years of
operation. A consumer group wants to investigate this statement. A random sample of n = 100 purchasers is selected
and each person is asked if the set purchased needed repair during the first 3 years. Let p denote the proportion of all
sets made by this manufacturer that will not need service in the first 3 years. The consumer group does not want to
claim false advertising unless there is strong evidence that p<0.90. The appropriate hypotheses are:
??: ? = 0.90
?1: ? < 0.90
a. In the context of this problem, describe a Type I error and its consequence.
b. In the context of this problem, describe a Type II error and its consequence.
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