Q18. - Algebra 1

Question

To predict whether or not an issue on a ballot will pass or fail, a committee randomly calls 250 houses with area codes that are inside the voting district and asks the opinions of registered voters. Based on these efforts, the committee determines that $71\%\left(\pm 2.5\%\right)$ of the voting population supports the issue. The committee concludes that the issue will pass.

a. Identify the sample.

b. Describe the population.

c. What method of data collection did the committee use: survey, experiment, or observational survey? Explain.

d. Is the sample biased or unbiased. Explain.

e. If unbiased, classify the same as simple, stratified, or systematic. Explain.

Step-by-Step Solution

Answer

a. The sample is randomly chosen 250 houses inside the voting district.

b. The population is the registered voters in the voting district.

c. The method of data collection used by the committee is: survey.

d. The sample is unbiased.

e. Sample is simple random sample.

Part a. Step 1. Define the concept of a sample.

A sample is a smaller portion of a larger group. This larger group is termed as population. A sample is selected to represent a certain portion, such that when analyzed and conclusions are drawn, those results then can be generalized for the entire population. Therefore, larger the sample size or the more samples taken the more closely it approximates the population.

Part a. Step 2. Example of a sample.

To determine whether the students like mathematics, the teachers ask a random sample of 50 students for their opinion.

Part a. Step 3. Identify the sample.

In the given case, to predict whether or not an issue on a ballot will pass or fail, a committee randomly calls 250 houses, therefore, the sample is randomly chosen 250 houses inside the voting district.

Part b. Step 1. Define the concept of a sample and population.

A sample is a smaller portion of a larger group. This larger group is termed as population. A sample is selected to represent a certain portion, such that when analyzed and conclusions are drawn, those results then can be generalized for the entire population. Therefore, larger the sample size or the more samples taken the more closely it approximates the population.

Part b. Step 2. Example of a population.

To determine whether the students in a school like mathematics, the teachers ask a random sample of 50 students for their opinion. Here the population will be all the students in the school.

Part b. Step 3. Describe the population.

In the given case, to predict whether or not an issue on a ballot will pass or fail, a committee randomly calls 250 houses, therefore, the sample is randomly chosen 250 houses inside the voting district. Since the sample consists of 250 houses with registered voters, thus, the population is the registered voters in the voting district.

Part c. Step 1. Define the concept of a sample and population.

A sample is a smaller portion of a larger group. This larger group is termed as population. A sample is selected to represent a certain portion, such that when analyzed and conclusions are drawn, those results then can be generalized for the entire population. Therefore, the larger the sample size or the more samples were taken the more closely it approximates the population.

Part c. Step 2. State types of samples.

Sample or the data collection techniques are:

1. Survey – Here data is from the responses of the sample.

2. Observational study – Here data is recorded after observing a sample.

3. Experiment – Here data is recorded after changing the sample.

Part c. Step 3. State the method of data collection.

In the given case, to predict whether or not an issue on a ballot will pass or fail, a committee randomly calls 250 houses, and they give their opinions, therefore, this is a survey.

Part d. Step 1. Define the concept of a sample and population.

A sample is a smaller portion of a larger group. This larger group is termed as population. A sample is selected to represent a certain portion, such that when analyzed and conclusions are drawn, those results then can be generalized for the entire population. Therefore, the larger the sample size or the more samples were taken the more closely it approximates the population.

Part d. Step 2. State the concept of the biased and unbiased sample.

If unbiased, then samples can be classified as:

1. Simple random sample – A sample that is equally likely to be chosen as any other sample from the population.

2. Stratified random sample – The population is first divided in similar, non-overlapping groups, then a random sample is selected.

3. Systematic random sample – A sample in which the items in the sample are selected according to a specified time or item interval.

Part d. Step 3. State the method of data collection.

In the given case, to predict whether or not an issue on a ballot will pass or fail, a committee randomly calls 250 houses. Since houses are chosen randomly, therefore, this sample is unbiased and the data collected through it will not be favoring a certain result and thus will not disrupt the results.

Part e. Step 1. State the concept of the biased and unbiased sample.

If a sample favors one group over another that the data are invalid because it is a biased sample. A sample is unbiased it is random.

Part e. Step 2. State types of unbiased sample.

Sample or the data collection techniques are:

1. Survey – Here data is from the responses of the sample.

2. Observational study – Here data is recorded after observing a sample.

3. Experiment – Here data is recorded after changing of the sample.

Part e. Step 3. State the type of unbiased sample.

In the given case, to predict whether or not an issue on a ballot will pass or fail, a committee randomly calls 250 houses, and they give their opinions, therefore, each member of the population of registered voters has an equal chance of getting selected, hence this is the simple random sample.