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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.
Women athletes at a certain university have a long term graduation rate of 67%. Over the past several years, a random sample of women athletes at the school showed that 23 eventually graduated. Does this indicate that the population of women athletes who graduate from the university is now less than 67%? Use a 10% level of significance.
a. State the null and alternate hypothesis
b. What sampling distribution will you use?
what is the value of the sample test statistic? (Round your answer to two decimal places)
c. Find the p-value of the test statistic. (Round your answer to four decimal places) sketch the sampling distribution and show the area corresponding to the p-value.
d. Based on your answers in part a to c, will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
e. Interpret your conclusion in the context of the application.
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