A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 15% of the women who actually have the disease. A new method has been developed that researchers claim will be able to detect cancer more accurately. A random sample of 80 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 9. (a) State the hypotheses and identify the claim. (b) Test the researchers' claim at the α = 0.05. Use the P-value method.
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 method currently used by doctors to screen women for possible breast cancer fails to
detect cancer in 15% of the women who actually have the disease. A new method has
been developed that researchers claim will be able to detect cancer more accurately. A
random sample of 80 women known to have breast cancer were screened using the new
method. Of these, the new method failed to detect cancer in 9.
(a) State the hypotheses and identify the claim.
(b) Test the researchers' claim at the α = 0.05. Use the P-value method.
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