High levels of blood sugar are associated with an increased risk of type 2 diabetes. A level higher than normal is referred to as “impaired fasting glucose.” An article reports a study in which 47 of 155 people with impaired fasting glucose had type 2 diabetes. Consider this to be a simple random sample. A doctor claims that less than 35% of people with impaired fasting glucose have type 2 diabetes. With what level of confidence can this claim be made? (Express the final answer as a percent.)
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.
High levels of blood sugar are associated with an increased risk of type 2 diabetes. A level higher than normal is referred to as “impaired fasting glucose.” An article reports a study in which 47 of 155 people with impaired fasting glucose had type 2 diabetes. Consider this to be a simple random sample.
A doctor claims that less than 35% of people with impaired fasting glucose have type 2 diabetes. With what level of confidence can this claim be made? (Express the final answer as a percent.)
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