JustAnswer
Answer the following problems showing your work and explaining (or analyzing) your results.
1. Define the following terms in your own words.
• Population
• Sample
• Bias
• Design
• Response bias
2. 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.
No, this is not random sampling, or the special case of simple random sampling. In this procedure, the population (homeowners in the city) is first sorted by spelling of given name, then systematically sampled. In a random sample, each member of the population has some probability of being selected. This is not true in this case. For example, people with last names beginning with O, Mc or Mac may never be reached if the city is much larger than 2,500 people (as most cities are). This can impart an ethnic bias to the selection.
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.
If freshmen are considered part of the population (as one would naturally assumed), then this is a misapplication of stratified sampling. In stratified sampling, the population is first divided into strata and then each strata (class) is sampled separately. This is essentially done here, samping one-tenth of each of the three upper classes. However, in a correct application of stratified sampling, the strata must be defined in a way to be exclusive and exhaustive, meaning every individual must belong to exactly one stratum. This is not true here, since a freshman does not belong to any of the defined strata.
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.
I would choose stratified random sampling. I would divide the employees into strata by gender or perhaps division (assuming there are only a few divisions of the company, since we have only 100 surveys to administer). I would then randomly choose individuals from each designated groups.
Stratified random sampling is preferred over simple random sampling because it produces more accurate estimates of the population’s characteristics, as well as providing insight into any potential differences between the strata.
b) Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.?
The population is all employees. The sample group is the set of individuals chosen to complete the survey. I would try to include every employee.
c) Discuss the bias, on the part of both the researcher and participants.
Participant bias is difficult to overcome in this case. For example, workers who are dissatisfied may be reluctant to be honest for fear of reprisal, and if the survey is optional, respondents will tend to be the less busy employees. Design of the survey can reduce this to some extent, but it is difficult to completely remove it.
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% (800/25,000) were returned. The results found that 92% (736/800) of people did not sell their house in the past 6 months and 85% (680/800) 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.
The survey described here is a voluntary sample, not a random sample, and therefore admits a likelihood of bias. Simply put, the people who have a very strong opinion about the topic are more likely to respond.
b) Should the writer conclude that the housing market is declining based upon this data?
No. This survey does not provide sufficient evidence to support (or refute) this claim.
c) Why or why not?
Because the sampling procedure is biased, no conclusion can be drawn about the results. A survey using random sampling would provide a more accurate estimate of the population, but even so, the use of personal opinions to gauge the market is in and of itself flawed, and highly unreliable. It would be much preferred to utilize true market data.
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