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Mathematics & Economics
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Math Problem
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Trident University Case

Math Problem Instructions:

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.
Answer the following problems showing your work and explaining (or analyzing) your results.
Define the following terms in your own words.
Population
Sample
Bias
Design
Response bias
Define and provide an example for each design method.
Simple random sampling
Systematic sampling
Stratified sampling
Cluster sampling
Choose one design method from the list above. Using your example, make a list of 2-3 advantages and 2-3 disadvantages for using the method.
The name of each student in a class is written on a separate card. The cards are placed in a bag. Three names are picked from the bag. Identify which type of sampling is used and why.
A phone company obtains an alphabetical list of names of homeowners in a city. They select every 25th person from the list until a sample of 100 is obtained. They then call these 100 people to advertise their services. Does this sampling plan result in a random sample? What about a simple random sample? Explain why or why not.
The manager of a company wants to investigate job satisfaction among its employees. One morning after a meeting, she talks to all 25 employees who attended. Does this sampling plan result in a random sample? What type of sample is it? Explain.
An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects 10 schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? What type of sample is it? Explain.
Fifty-one sophomore, 42 junior, and 55 senior students are selected from classes with 516, 428, and 551 students respectively. Identify which type of sampling is used and explain your reasoning.
You want to investigate the workplace attitudes concerning new policies that were put into effect. You have funding and support to contact at most 100 people. Choose a design method and discuss the following:
Describe the sample design method you will use and why.
Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.?
Discuss the bias, on the part of both the researcher and participants.
A local newspaper wanted to gather information about house sales in the area. It distributed 25,000 electronic surveys to its readers asking questions about house sales in the past 6 months. Of the surveys sent out, 3.2% were returned. The results found that 92% of people did not sell their house in the past 6 months and 85% of people would expect a loss if they sold their house. The writer wants to use these results to conclude that the housing market is declining, and we are headed for a recession.
Explain the bias and sampling error in this study.
Should the writer conclude that the housing market is declining based upon this data?
Why or why not?

Math Problem Sample Content Preview:

Module 4 - Case SAMPLING
Name:
Course:
Trident University
Instructor:
Date:
Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.
Answer the following problems showing your work and explaining (or analyzing) your results.
Define the following terms in your own words.
Population- this represents all the observations or elements from a data set.
Sample- this is a subset of the whole population, and larger unbiased samples provide the best information from which to draw conclusions about the population.
Bias- this represents the error in a sample, selection and it is the difference between the expected value and the actual values for the target populations.
Design- This is a detailed plan on how one seeks to undertake a research and investigation, including the data collection and method of analyzing the data.
Response bias- this is the risk that there will be bias by respondents in a survey study, who might not provide truthful responses to the questions
Define and provide an example for each design method.
Simple random sampling- A sample is chosen randomly with every individual element having an equal chance of beings elected. An example of simple random sampling is to selecting workers in an office randomly, with a view of understanding those who have experienced workplace violence.
Systematic sampling- in this design method, the first element is chosen randomly and then the others are chosen for every nth subject from the set of data. For instance, a researcher studying the prevalence of flu in a cold season has 100 study participants, and the researcher chooses every 5th person among the study participants.
Stratified sampling- this approach focuses on dividing the population into sub population groups, and elements are chosen from the sub groups. For instance, a study to understand whether customers have had positive or negative experience with online shopping, whereby there is sample of 1,000 individuals divided into 500 males and 500 females
Cluster sampling- this is a sampling approach where the target population is divided into clusters with similar profiles, this is especially when the population is large. For example, a study to study the average salaries of accountants with the clusters being the accounting firms.
Choose one design method from the list above. Using your example, make a list of 2-3 advantages and 2-3 disadvantages for using the method.
Cluster sampling
Advantages
It eliminates the risk of systematic bias.
It is easy and convenient to use.
Disadvantages
In some instances it may be difficult to divide the population into appropriate cluster groups.
When there are huge differences among members of a unit, the approach is less effective.
There is also a risk that the estimates based on the clusters are likely to be less precise.
The name of each student in a class is written on a separate card. The cards are placed in a bag. Three names are picked from the bag.  Identify which type of sampling is used and why.
This approach is the simple random sampling as each card containing the student name has an equal opportunity of being chose...
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