Researchers at Purdue University and Wichita State University found that airlines are doing a better job of getting passengers to their destinations on time (Associated Press, April 2, 2012). AirTran Airways and Southwest Airlines were among the leaders in ontime arrivals with both having 88% of their flights arriving on time. But for the 12% of flights that were delayed, how many minutes were these flights late? Sample data showing the number of minutes that delayed flights were late are provided in the sheet named AirDelay. Data are shown for both airlines. (a) Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (b) What is the sample mean number of minutes late for delayed flights for each of these two airlines? (c) Using a 0.05 level of significance, what is the p-value and what is your conclusion
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.
Researchers at Purdue University and Wichita
State University found that airlines are doing a better job of getting passengers to
their destinations on time (Associated Press, April 2, 2012). AirTran Airways and
Southwest Airlines were among the leaders in ontime arrivals with both having 88%
of their flights arriving on time. But for the 12% of flights that were delayed, how
many minutes were these flights late? Sample data showing the number of minutes
that delayed flights were late are provided in the sheet named AirDelay. Data are
shown for both airlines.
(a) Formulate the hypotheses that can be used to test for a difference between the
population mean minutes late for delayed flights by these two airlines.
(b) What is the sample mean number of minutes late for delayed flights for each of
these two airlines?
(c) Using a 0.05 level of significance, what is the p-value and what is your conclusion?
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