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The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the portion of students at her university who visited campus bars every weekend.  Her advisor took a random sample of 250 students.  The total number of students in the sample who visited campus bars every weekend is an example of :Question 23Answera. a categorical random variable.b. a discrete random variable.c.a parameter.d.a continuous random variable

Question

The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the portion of students at her university who visited campus bars every weekend.  Her advisor took a random sample of 250 students.  The total number of students in the sample who visited campus bars every weekend is an example of :Question 23Answera. a categorical random variable.b. a discrete random variable.c.a parameter.d.a continuous random variable

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Solution

The answer is b. a discrete random variable.

Here's why:

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types of random variables, discrete and continuous.

a) A categorical random variable would be applicable if the data could be divided into categories. For example, if the students were categorized as "visits bars" and "does not visit bars".

b) A discrete random variable is a variable that can take on a countable number of values. The number of students who visit campus bars every weekend is countable, hence it is a discrete random variable.

c) A parameter is a numerical characteristic of a population. In this case, the total number of students who visit campus bars every weekend is not a characteristic of the entire student population, but rather a characteristic of the sample.

d) A continuous random variable is a variable that can take on an infinite number of values within a certain range. The number of students who visit campus bars every weekend is not continuous because it cannot take on an infinite number of values.

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