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Problem 6 Medium Difficulty

Indicate which of the following situations involve sampling from a finite population and which involve sampling from an infinite population. In cases where the sampled population is finite, describe how you would construct a frame.
a. Select a sample of licensed drivers in the state of New York.
b. Select a sample of boxes of cereal off the production line for the Breakfast Choice Company.
c. Select a sample of cars crossing the Golden Gate Bridge on a typical weekday.
d. Select a sample of students in a statistics course at Indiana University.
e. Select a sample of the orders being processed by a mail-order fim.

Answer

a. Finite, because there will exist a list of all licensed drivers in the state of New York.
Select a random number between 0 and 1 for each licensed drivers.
The sample will then consist of the licensed drivers with the smallest random numbers.
b. Infinite, because we cannot determine every single box that the Breakfast Choice Company has produced (present and future), moreover the population will increase every single day.
c. Infinite, because we cannot determine every car that crosses the bridge (present and future), moreover the population will increase every single day.
d. Finite, because there students in a statistics course at one university will be a relatively small group.
Select a random number between 0 and 1 for each student in a statistics course.
The sample will then consist of the students with the smallest random numbers.
e. Infinite, because we cannot determine every order that is being processed by a mail-order firm (present and future), moreover the population will increase every single day.

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Video Transcript

all right, So this question gives us a variety of scenarios and wants us to determine whether each represents a finite or infinite population. And if it's finite, described a sampling procedure. So part eh asks about drivers in the state of New York, and that is a finite population. Because if you think about it, there's definitely a database that has all the New York drivers in it, So that means we can create a sample from that. So how do we do that? Well, looking at our sampling procedure, we see that we should first number every driver in the state of New York from one to capital and where capital ends the total number of drivers. Then, for each number in the list, we generate a random number for each between zero and one, and then we select the lower case and smallest elements where lower case and is our sample size. No part B asks us about boxes of cereal off a production line and that we consider an infinite population because there's so many cereal boxes in circulation and it changes every day. Some are being thrown out while more being made, so the population sizes rapidly fluctuating, and it's hard to keep track of every single cereal box by number. There's very little you can do to uniquely identify each cereal box, so we say it's infinite. Then part See asks about traffic on the bridge and this for similar reasons. We also say is infinite because there's so many different cars coming by that it's very hard to uniquely identify each car and give it a specific number in a population. And it's constantly changing and growing, so we call that infinite as well. Them. We have students in a specific statistics class, and this is finite because if they're students taking this class, then it's definitely kept track of in the universities database, and each student can easily be identified by name uniquely so. From there, we could make a sample by numbering each student from one end than generating a random number for each student, and then we pick the smallest number for our sample. Depending on how big we want it, we take the smallest end. Then, finally, for party, a mail order company. We'll say that this is infinite because there's so many orders being processed