# Define the Following Terms in Words (Math Problem Sample)

Sampling

Case Assignment Module 4

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

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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:

a. Describe the sample design method you will use and why.

b. Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.?

c. Discuss the bias, on the part of both the researcher and participants.

10. 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.

a. Explain the bias and sampling error in this study.

b. Should the writer conclude that the housing market is declining based upon this data?

c. Why or why not?

source..Case Assignment Module 4 sampling

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Define the following terms in your own words.

•Population- This encompasses all the elements of the data set that are taken into account in a research study.

•Sample- This is a subset of a population that contains one or more of the observations

•Bias- This refers to the systematic errors that underestimate or overestimate the actual value of a population parameter, meaning that the outcomes misrepresent the population characteristics.

•Design- This is the plan detailing the sampling approach and encompasses the factors that influence sampling

•Response bias- This the error related to the study participants providing inaccurate responses, and this is especially studies considering voluntary participation, whereby the participants have strong opinions about a subject

Define and provide an example for each design method.

•Simple random sampling- This is the study design method that each and every element in the target population has the same probability of being selected from a sample

•Systematic sampling- In this approach, after selecting the first element randomly, the next selections are chosen for every nth value in the target population.

•Stratified sampling- This is a sample design whereby the target population is divided into non-overlapping strata/subpopulations/groups based on specific criteria

•Cluster sampling- The population is placed into groups of clusters, which contain elements that are not necessarily the same size. Since each element belongs to a cluster, it is the clusters that are sampled rather than the elements.

3. 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.

Stratified sampling

Advantages

Estimates for the subpopulation means and variance are readily available

For each sample size stratified sampling produces fewer sampling errors compared to cluster sampling and random sampling.

It is appropriate to use a small sample size when using the stratified sampling design.

Disadvantage

There is risk that inaccuracies in determining the appropriate size of strata.

It may be necessary to calculate the required population strata numbers.

4. 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 is simple random sampling since there is an equal chance that each student’s name will be chosen, if a card is selected from the bag.

5. 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.

This is not a case of either a random sampling or simple random sampling. There is no randomness i...

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