The health department wants to estimate the proportion of eggs shipped by a large egg producer that contain salmonella. The inspector takes a random sample of 1100 eggs from all the eggs shipped in one week and determines that 12 of the 1100 eggs tested have salmonella. a) Calculate a 95% confidence interval for the proportion of eggs shipped by this producer that contain salmonella. Conduct a complete analysis and interpret your interval in the context of the health department’s objective. b) What is the margin of error for the interval estimate that you generated in part a? c) Based on your estimate, is it plausible (at a 95% confidence level) that the proportion of eggs produced by this supplier that has salmonella is greater than 1.5%? Why or why not?
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.
The health department wants to estimate the proportion of eggs shipped by a large egg producer that contain salmonella. The inspector takes a random sample of 1100 eggs from all the eggs shipped in one week and determines that 12 of the 1100 eggs tested have salmonella.
a) Calculate a 95% confidence interval for the proportion of eggs shipped by this producer that contain salmonella. Conduct a complete analysis and interpret your interval in the context of the health department’s objective.
b) What is the margin of error for the
c) Based on your estimate, is it plausible (at a 95% confidence level) that the proportion of eggs produced by this supplier that has salmonella is greater than 1.5%? Why or why not?
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