Homecoming. A college Statistics class conducted a survey concerning community attitudes about the col-lege’s large homecoming celebration. That survey drew its sample in the following manner: Telephone numberswere generated at random by selecting one of the localtelephone exchanges (first three digits) at random andthen generating a random four-digit number to followthe exchange. If a person answered the phone and thecall was to a residence, then that person was taken to bethe subject for interview. (Undergraduate students andthose under voting age were excluded, as was anyonewho could not speak English.) Calls were placed until asample of 200 eligible respondents had been reached.a) Did every telephone number that could occur in thatcommunity have an equal chance of being generated?b) Did this method of generating telephone numbersresult in a simple random sample (SRS) of localresidences? Explain.c) Did this method generate an SRS of local voters?Explain.d) Is this method unbiased in generating samples ofhouseholds? Explain.
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.
lege’s large homecoming celebration. That survey drew
were generated at random by selecting one of the local
telephone exchanges (first three digits) at random and
then generating a random four-digit number to follow
the exchange. If a person answered the phone and the
call was to a residence, then that person was taken to be
the subject for interview. (Undergraduate students and
those under voting age were excluded, as was anyonewho could not speak English.) Calls were placed until a
sample of 200 eligible respondents had been reached.
a) Did every telephone number that could occur in that
community have an equal chance of being generated?
b) Did this method of generating telephone numbers
result in a simple random sample (SRS) of local
residences? Explain.
c) Did this method generate an SRS of local voters?
Explain.
d) Is this method unbiased in generating samples of
households? Explain.
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