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Exercise 3: Determining Sample Size

by | May 22

1. We need to draw a random sample of undergraduate students from a population of 8,943 students enrolled at University Park campus of the Pennsylvania State University. Compute the needed sample size for each scenario presented in Table 1.
Table 1: Estimating Sample Size
Sampling Error Risk P Q Sample Size
1. 4% 5% .6 .4 __________
2. 5% 1% .4 .6 __________
3. 3% 5% .6 .4 __________
4. 4 % 1% .6 .4 __________
5. 3% 5% .3 .7 __________
6. 4% 5% .2 .8 __________
7. 4% 1% .3 .7 __________
8. 5% 5% .55 .45 __________
9. 5% 5% .25 .75 __________
10. 4% 5% .85 .15 __________
2. What type of sample would you have if you first group the 4-H members by ethnicity (African American, Asian American, Hispanic/Latino, and white), and then randomly draw your sample based on the proportion of members in each category?
a. Cluster/multistage random sampling
b. Simple random sampling
c. Stratified random sampling
d. Systematic random sampling
3. Rama Radhakrishna is interested in knowing what graduate alumni of Agricultural and Extension Education Department at Penn State who graduated between the years 1980-2002 are doing? He gets the roaster of names of the AEE alumni from Betty Blair, selects the names of 120 individuals from the roaster using a table of random numbers, and then mails a questionnaire to everyone selected. Which of the following sampling types that Rama should use?
a. Cluster/multistage random sampling
b. Simple random sampling
c. Stratified random sampling
d. Systematic random sampling
4. Laura Dinnini is interested in researching the best restaurants in State College based on the opinions of food critics. She begins by asking her advisor, who refers the student to four food critics who have written extensively on the subject and whom the student then contacts to interview for her study. Identify the sampling method used by Ms. Dinnini
a. Random sample
b. Nonrandom sample
c. Simple random sample
5. A researcher is interested in identifying the attitudes of physicians who work for Geisinger Medical centers in Pennsylvania toward the Republican plan for health care. She obtains the list of all Geisinger groups and randomly selects five of the centers. Then she obtains the list of all the physicians at these five centers and randomly selects eight physicians from each centre to interview. Identify the sample type used by the researcher.
a. Stratified random sample
b. Cluster sample
c. Nonrandom sample
d. Two-stage random sample
6. Heather Jones as president of AEE Graduate Student Association is interested in determining how other graduate students of AEE program feel about the program. She interviews all of the students she has access to on a Monday night outside the Ag Administration Building. Identify the type of sample that Heather is using.
a. Stratified random sample
b. Simple random sample
c. Convenience sample
d. Purposive sample
7. A high school agricultural teacher interviews all of the students who are members of the FFA. What type of sample did the high school ag teacher use?
a. Purposive
b. Simple random sample
c. Convenience sample
d. Census
8. The Pennsylvania Agricultural Education Teacher Directory is your sampling frame. You decide to draw every 8th name after using a random start. What type of sample would you have?
a. Purposive
b. Simple random sample
c. Systematic random sample
d. Stratified random sample
9. The population of Extension agents in the United States is divided into four Extension Regions (East, North, South, West). The population sizes of agents in each of the regions are as follows: Eastern – 830, Northern–660, Western–480, and Southern—1030. A sample of 450 is to be selected. Using stratified sampling procedure with proportional allocation, determine the sample size you would suggest for each strata (region).
10. The Ferguson township of State College would like to conduct a survey of its residents and has a list of 5,000 registered voters (frame). The township needs your help in calculating the sample size using systematic sampling procedures. Describe the process (risk, sampling error, variability, sampling interval, etc.) you would use to determine the sample size.
11. Your instructor for the class want to conduct a study that involves surveying a large population (for example Center County Residents). The county has five school districts (strata). The population of each school district are as follows:
Strata 1 5,000
Strata 2 16,000
Strata 3 7,000
Strata 4 5,000
Strata 5 9,000
What is the sampling fraction for each strata?
From whom you will collect data and why?
What sample size you would recommend and why? Include sampling error, risk, and variability?
What sampling method you would recommend to use and why? If you select, stratified random sampling, you must show calculations for determining sampling size for each strata or district
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