Q18. - Algebra 1

Question

To estimate who the leading candidate is, the candidates’ committee surveys a large group of people selected at random. The returns indicate that their candidate is leading 58% to 42%.

 

1. Identify the sample. Suggest a population from which the sample was selected.
2. State the method of data collection.
3. Is the sample biased or unbiased? Explain.
4. If unbiased, classify the random sample as simple, stratified or systematic.

Step-by-Step Solution

Answer

1. The sample is people who take part in the survey. Population is All people who vote.
2. The method of data collection is a survey.
3. The sample is biased.
4. The sample cannot be classified.

 

Step 1. State the concept for sampling.

A sample is a specific group that you will collect data from. The size of the sample is always less than the total size of the population. 

Sampling is the process or method of selecting samples from a population based on some rules or criteria. The sampling method depends on the type of analysis that is going to be done on the population. It may be simple random sampling or systematic sampling or stratified sampling.

Step 2. State the definition for simple, stratified and systematic sampling .

A simple random sample is a randomly selected sample from the population that is used to represent the entire data population.

A stratified sample is a random sample that is taken from the population in which the population is partitioned into relatively homogeneous groups called strata.

Systematic sampling can be defined as a method of probability sampling of a large population via fixed, repeated intervals.

Step 3. State the concept for biased and unbiased samples .

A biased sample means the sample is not representative of the population, which means the method for getting the sample is defective.

An unbiased sample means the sample is representative of the population.

Step 4. State the answer with an explanation .

People who take part in a survey are a sample from the whole population of all people who vote.

Since data is collected through responses from a sample of the population, it is a survey. This data allows the committee to draw a conclusion about the leading candidate.

Also, since data is collected from a large population, and not everyone is a voter, the sample is biased. The opinions of the non-voters will not matter and this will affect the result of the survey.

As the sample is biased, it cannot be classified as simple, stratified or systemic.