For problems 1 -6, describe the type of sampling being considered by a school bo
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Question
For problems 1 -6, describe the type of sampling being considered by a school board for a county system with 45 schools to get feedback from teachers on an important issue:
a. Simple Random Sample d. Systematic
b. Stratified e. Convenience
c. Cluster
1. They randomly select 9 schools and interview all of the teachers in those schools.
2. The school board secretary stands in the lobby area after a county wide teachers’ meeting and stops some of the teachers as they leave for lunch to interview them.
3. The school board could list all of the schools alphabetically and select every 5th school on the list.
4. The school board could take a list of all teachers listed alphabetically, assign each teacher a three digit number, and randomly select 100 teachers to interview.
5. The school board decides that the teachers at different school levels will have a different opinion. This district has 30 elementary schools, 10 middle schools and 5 high schools. Therefore, they design the study so that they randomly select 6 elementary schools, 2 middle schools and 1 high school (20% of each type) and interview all of the teachers of those selected schools.
6. With the same school board as in the problem above, the board decides to do a multistage sampling method. They are going to randomly pick 9 schools and then select 2 teachers from each grade level at each school to interview. Which two sampling methods listed above are being used?
For problems 7-8: A popular website places opinion poll questions next to many of its news stories. A participant simply clicks their response to join the sample. One of the questions in January 2008 was “Do you plan to diet this year?” More than 30,000 people responded, with 68% saying “yes.”
7. What type of bias would this poll represent? (Explain your answer)
8. What can you conclude?
a. about 68% of Americans like to diet
b. the results tell us little about the population because of bias
c. the sample is too small to draw a conclusion
9. There are twenty-eight schools in the Bugsland School District. The superintendent wants to pay a surprise inspection on four of those schools. He numbers the school 1 – 28 after listing them alphabetically and then uses a random number table to select four schools. Using the seed number of 15, which numbers would represent the schools he selects?
10. A sample produced a list of 100 licensed drivers. The investigators now want to choose a SRS of 5 of these drivers to answer questions about their driving habits. They number the drivers 1 – 100. Using the seed number 37, which numbers would represent the five drivers selected?
For problems 11-12: The Ministry of Health in the Canadian province of Ontario wants to know whether the national health care system has achieved its goals in the province. Much information about health care comes from patient records but that source doesn’t allow us to compare people who use health services with those who don’t. So the Ministry of Health conducted the Ontario Health survey, which interviewed a random sample of 61,239 people who live in Ontario.
11. What is the population for this sample survey?
12. What is the sample for this sample survey?
a. The entire population of Ontario
b. The people who refused or could not participate
c. The 61, 239 people who were interviewed.
Matching: For each definition/description given, identify the term that it represents. Use the following to choose from.
a. parameter c. sampling bias
b. discrete variable d. quantitative variable
13. An error in gathering data that makes the results questionable as to its usefulness in evaluating the observation.
14. A variable that tells how much or how many of something there is
15. A number that describes the population
16. A quantitative variable whose possible values can be listed.
More sampling: Use the following sampling methods to describe the type of sampling represented in the following problems.
a. Simple Random Sample d. Systematic
b. Stratified e. Convenience
c. Cluster
17. An education researcher randomly selects 38 schools from one school district and interviews all the teachers at each of the 38 schools. Identify the type of sampling used in this example.
18. At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school administrator selects a random sample of 12 of the freshmen, a random sample of 9 of the sophomores, a random sample of 11 of the juniors, and a random sample of 8 of the seniors. She then interviews all the students selected. Identify the type of sampling used in this example.
19. Before premiering a blockbuster movie at a theater, test screenings are done beforehand. Each theater premiering the movie is supposed to interview every 20th person as they leave the theater when the movie over. Identify the type of sampling used in this example.
20. A biology teacher wants to know how the students in her department feel about a certain course sequence. She takes a list of students in her department in which the students are numbered as they are listed in alphabetical order. She uses a random number generator to select 40 numbers and interviews the students that those numbers represent in the alphabetical listing. Identify the type of sampling used in this example.
21. The cafeteria decides to change their menu selection. To determine possible new menu items they interview every 10th student that checks out of the cafeteria line on a given day. Identify the type of sampling used in this example.
Types of Bias
22. Inside the boxes of a new brand of cereal, is a short survey that can be mailed back for free to the manufacturer. The survey asks the consumer if he or she likes the cereal or not. What, if any, will be the most noticeable bias for this survey?
Voluntary response bias
Undercoverage of the population
There does not seem to be any bias
23. A newspaper reporter decided to sample residents of all major metropolitan areas in the entire country. This sampling asked if the residents liked living in their city, or are they considering moving, and if so, where? Unfortunately, this survey went over budget and was stopped and only the East coast was adequately interviewed. With regards to having this survey labeled as representing the entire country what, if any, will be the most noticeable bias for this survey as it is now?
Voluntary response bias
Undercoverage of the population
There does not seem to be any bias
For each variable below, indicate whether it is quantitative or categorical. If quantitative, include whether it is discrete or continuous. If categorical, indicate whether it is nominal or ordinal.
24. income 25. political party affiliation
26. t-shirt size (S, M, L, SL) 27. number of votes per candidate
28. wingspan of butterflies 29. movie ratings (G, PG, etc.)
30. There were 60 patients participating in a new treatment program. Assume the patients have been assigned a number between 1 and 60. The researcher wants to interview the families of 4 patients to get their impression of patient care. Using a seed of 16, use a random number generator on the calculator to select the four patients for the study.
A local high school is interested in the students’ opinion about having pep rallies. There are 1452 students in the school. One hundred students are selected and interviewed. Which value is a parameter and which one is a statistic?
Use this stem & leaf plot to answer the following:
24
0 2 3
24
9
25
1 1 4
25
7 8 8 9
26
0 0 1 1 3
26
5 5 6 7 8 9
List the original data
Describe the shape of the distribution
24
0 2 3
24
9
25
1 1 4
25
7 8 8 9
26
0 0 1 1 3
26
5 5 6 7 8 9
Explanation / Answer
24) income is a quantitative and continuous
25) qualitative and categorical
26) t shirt -qualitative and nominal
27) quantitative and discreet
28) quantitative and discreet
29) qualitative and ordinal
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