# Mathematics

Assignment

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.

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:

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

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

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

1. 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.

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

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

j. Why or why not?

1. Using the same data example collected in the first assignment, you will continue to collect data for another 5–10 days. Write a paper (1–3 pages) including all of the following content:

a. Recalculate the mean, standard deviation, and variance.

b. Is your mean increasing or decreasing?

c. Explain the effects of the larger sample size in relation to your data.

d. Do you think the current sample you have is enough to draw an accurate conclusion, or do you need a larger sample?

e. What conclusions can you draw from comparing both sets of data?

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