Question

The administration at a high school with 1800 students wants to gather student opinions about parking for students on campus. It isn’t practical to contact all students.

a. Give an example of a way to choose a voluntary response sample of students. Explain how this method could lead to bias.

b. Give an example of a way to choose a convenience sample of students. Explain how this method could lead to bias.

c. Describe how to select an $\mathrm{SRS}\mathrm{of}50$students from the school.

d. Explain how the method you described in part (c) avoids the biases you described in parts (a) and (b).

Short answer

a. The answer could vary for example online poll of a way to choose a voluntary response sample of students.

b. The answer could vary for example the first $50$students who arrive on the campus on a particular day of a way to choose a convenient sample of students.

c. The answer is, let us assign a unique number $1\mathrm{and}1800$to each student.

d. The sample random sample will also not suffer from nonresponse bias, assuming that we are capable to contact all the samples and get each of their opinions.

Step-by-step solution

Part (a) step 1: Given Information

We need to give an example of a way to choose a voluntary response sample of students. Explain how this method could lead to bias.

Part (a) step 2: Explanation

A voluntary response sample is a sample for which the subjects can decide if want to be in the sample or not.

The nonresponse bias is a result of not having data for everybody in the sample.

Now, we can create a voluntary response sample by posting an online poll on the website of high school on which students will need to voluntarily share their own opinion. So, people with the strongest opinions tend to participate in voluntary response samples, the opinion in many samples are often not representative of the entire population.

Other ways to create a voluntary response sample include students needing to make a call or send a letter to share their opinion.

Part (b) step 1: Given Information

We need to give an example of a way to choose a convenience sample of students. Explain how this method could lead to bias.

Part (b) step 2: Explanation

Convenience sampling uses a subgroup from the population, is conveniently chosen.

Selection or undercoverage bias will include part of the population. Convenience samples suffer from undercoverage bias.

A possible way to choose a convenience sample is by selecting the first $50$students who arrive on the campus on a particular day, which will not be representative for the population as these first $50$are more likely to have a parking spot and thus will have different opinions form those who do have a parking spot when arriving at school.

Other possible way to choose a convenience sample is by selecting one class to be in the sample.

Part (c) step 1: Given Information

We need to find to select an $\mathrm{SRS}\mathrm{of}50$student from the school.

Part (c) step 2: Explanation

Simple random sampling users a sample of size $\mathrm{n}$in which every sample size $\mathrm{n}$has an equal chance of being chosen.

The high school has$1800$students and we want to select a simple random sample$\left(\mathrm{SRS}\right)\mathrm{of}50$of students from these$1800$students.

Now, let us assign a unique number between $1\mathrm{and}1800$to each student.

Let us use the random digits table in the appendix to select the students in the sample. Choose a row form which to start in the table.

Select the first $4-\mathrm{digit}$number. If the number is between$1\mathrm{and}1800$, then select the corresponding student to be in the sample, else ignore the number and select the next $4-\mathrm{digit}$number. Repeat until unique students were selected to be in the sample.

Part (d) step 1: Given Information

We need to explain that the method you described in part (c) avoids the biases you described in parts (a) and (b).

Part (d) step 2: Explanation

Simple random sampling uses a sample size$\mathrm{n}$in which every sample of size has an equal chance of being chosen.
Selection or under coverage bias will exclude part of the population.
Nonresponse bias is a result of not having data for everybody in the sample.
A simple random sample will not suffer from under coverage bias, because the simple random sample is selected from the population and thus nobody was excluded from being in the sample.

A simple random sample will also not suffer from nonresponse bias, assuming that we are capable to contact all the students in the sample and get each of their opinions.