College Board, the company that runs AP testing, wants to expand access to AP courses. Some schools require that students take the AP exam at the end of the course while others leave the AP exam as optional. A random sample of 200 students from schools where AP exams are required had 84 students currently enrolled in at least one AP course. Another random sample of 190 students from schools where the AP exam is optional had 98 students currently enrolled in at least one AP course. (a) College Board want to test the claim that requiring the AP exam lowers the proportion of students who enroll in at least one AP course. Carry out a test of this claim at the 5% level of significance. (b) Based on your decision in part (a), what error may have been made, a Type I or Type II error? Give a consequence of that error. (c) Interpret the p-value from part (a) in the context of this question.
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.
College Board, the company that runs AP testing, wants to expand access to AP courses. Some schools require that students take
the AP exam at the end of the course while others leave the AP exam as optional. A random sample of 200 students from schools
where AP exams are required had 84 students currently enrolled in at least one AP course. Another random sample of 190
students from schools where the AP exam is optional had 98 students currently enrolled in at least one AP course.
(a) College Board want to test the claim that requiring the AP exam lowers the proportion of students who enroll in at least one
AP course. Carry out a test of this claim at the 5% level of significance.
(b) Based on your decision in part (a), what error may have been made, a Type I or Type II error? Give a consequence of that
error.
(c) Interpret the p-value from part (a) in the context of this question.
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