A computer software magazine compares the rates of malware infection for computers protected by security software A with the rates of infection for computers protected by security software B. They found that out of 787 computers with security software A, 72 became infected with some type of malware after 1000 hours of internet interaction. For security software B, 37 out of 834 computers became infected after 1000 hours of internet interaction. Assuming these to be random samples of infection rates for the two security software packages, construct a 98% confidence interval for the difference between the proportions of infection for the two types of security software packages. Interpret the results. Does the confidence interval contradict the claim that the proportion of infections is the same for the two types of security software?
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 computer software magazine compares the rates of malware infection for computers protected by security software A with the rates of infection for computers protected by security software B.
They found that out of 787 computers with security software A, 72 became infected with some type of malware after 1000 hours of internet interaction. For security software B, 37 out of 834 computers became infected after 1000 hours of internet interaction.
Assuming these to be random samples of infection rates for the two security software packages, construct a 98% confidence interval for the difference between the proportions of infection for the two types of security software packages. Interpret the results. Does the confidence interval contradict the claim that the proportion of infections is the same for the two types of security software?
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