Sampling, Hypothesis Testing, and Regression (Math Problem Sample)
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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.
- Choose one design method from the list below. Using your example, make a list of 2 or 3 advantages and 2 or 3 disadvantages for using the method. (2 pts)
- Simple random sampling
- Systematic sampling
- Stratified sampling
- Cluster sampling
- 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. (2 pts)
- 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 type of sample is it? Explain. (2 pts)
- 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. (2 pts)
- 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. (2 pts)
- 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. (2 pts)
- 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. (2 pts)
- Specify the population and sample group. Will you include everyone who works for the company, certain departments, full or part-time employees, etc.? (2 pts)
- Discuss the bias, on the part of both the researcher and participants. (2 pts)
- 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. (2 pts)
- Should the writer conclude that the housing market is declining based upon this data? (2 pts)
- Why or why not? (2 pts)
- A homeowner is getting carpet installed. The installer is charging her for 250 square feet. She thinks this is more than the actual space being carpeted. She asks a second installer to measure the space to confirm her doubt. Write the null hypothesis Ho and the alternative hypothesis Ha. (2 pts)
10. Drug A is the usual treatment for depression in graduate students. Pfizer has a new drug, Drug B, that it thinks may be more effective. You have been hired to design the test program. As part of your project briefing, you decide to explain the logic of statistical testing to the people who are going to be working for you.
. Write the research hypothesis and the null hypothesis. (2 pts)
- Then construct a table like the one below, displaying the outcomes that would constitute Type I and Type II error. (2 pts)
Write a paragraph explaining which error would be more severe, and why. (2 pts)
Case Assignment –
Sampling, Hypotheses Testing, and Regression
January 29, 2017
Your Institution of Affiliation
1 The Sampling method that I chose is Stratified sampling. The main advantages of Stratified Sampling as compared to others are: (1) Greater specificity and precision using the same number of sample population as compared to simple random sampling, (2) provides a better assurance that the sample population is “representative” of the variables being measured, and (3) better cost-efficiency in gathering data, since the size needed for measurement is smaller those of others CITATION Sta17 \l 1033 (Stattrek.com, 2017). On the other hand, some of the disadvantages of Stratified sampling are (1) the effort needed to supervise the process if much greater as compared to simple random sampling CITATION Sta17 \l 1033 (Stattrek.com, 2017) and (2) the data gathered has a ‘high-risk’ of usability given that the researchers are unable to correctly categorize the samples into their groups CITATION Inv15 \l 1033 (Investopedia.com, 2015).
2 In this case, the sampling method chosen is a Simple Random sampling. This is because the starting population, was not divided into subsets or subgroups (cluster and stratified), and they are not randomly selected from a given category (systematic). Thus, this shows that simple random sampling was utilized since each member of the class was simply given an equal probability to be chosen.
3 This case clearly shows a Systematic Sampling method. As stated in the case, the telephone company randomly chose the sample by first choosing the larger population (homeowners in the city), then selecting the population “according to a random starting point and a fixed periodic interval” (every 25th homeowner in the list) CITATION Invnd \l 1033 (Investopedia.com, n.d.). This method specifically defines what a Systematic sampling method is. In terms of its “randomness”, we could rest assure that the data would stay that way despite the use of a ‘fixed point interval’, since the method does not pinpoint any exact subgroup or population.
4 In this case, I could argue that the sample is most probably an “unrepresentative sample”. This is because of the possibility that those who attended are only the ones who are “satisfied” with their works or the other way around (non-response bias). Nonetheless, this could still be seen as a random sample since the members who attended were not classified into distinct categories (e.g. both satisfied and not).
5 The case presented is a clear example of a ‘Stratified random sampling’ since the education expert started by choosing a particular district, before selecting randomly from the specified population. In other words, the education expert created a ‘strata’ in order to facilitate the sample selection process. Nevertheless, this is a type of ‘stratified sampling’ which results in a random population since the groups (all teachers in the selected schools) are randomly selected in a higher stratum (district level).
6 This case exhibits the process of “Cluster Random Sampling”. As stated in the case, a number of students are chosen from different year levels. In this case, the students are chosen within a larger population, in order to create clusters or subgroups (e.g. 42 junior students). A technique only utilized by Cluster sampling.
7 Study of workplace attitudes concerning new policies
1 In this case, the best sample design method to use is the “stratified sampling method”. This is due to the fact that this workplace has a lot of other departments and sub-departments and thus, using any other types could easily lead to an “unrepresentative sample” of all ...
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