The next four questions refer to the following: A Lake Tahoe Community College instructor is interested in the average number of days Lake Tahoe Community College math students are absent from class during a quarter.
Exercise 19
What is the population she is interested in?
- A. All Lake Tahoe Community College students
- B. All Lake Tahoe Community College English students
- C. All Lake Tahoe Community College students in her classes
- D. All Lake Tahoe Community College math students
Solution
D
Exercise 20
Consider the following:
In this case,
- A. Variable
- B. Population
- C. Statistic
- D. Data
Solution
A
Exercise 21
The instructor takes her sample by gathering data on 5 randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is
- A. Cluster sampling
- B. Stratified sampling
- C. Simple random sampling
- D. Convenience sampling
Solution
B
Exercise 22
The instructor’s sample produces an average number of days absent of 3.5 days. This value is an example of a
- A. Parameter
- B. Data
- C. Statistic
- D. Variable
Solution
C
The next two questions refer to the following relative frequency table on hurricanes that have made direct hits on the U.S between 1851 and 2004. Hurricanes are given a strength category rating based on the minimum wind speed generated by the storm. (http://www.nhc.noaa.gov/gifs/table5.gif [link])
Category | Number of Direct Hits | Relative Frequency | Cumulative Frequency |
---|---|---|---|
1 | 109 | 0.3993 | 0.3993 |
2 | 72 | 0.2637 | 0.6630 |
3 | 71 | 0.2601 | |
4 | 18 | 0.9890 | |
5 | 3 | 0.0110 | 1.0000 |
Total = 273 |
Exercise 23
What is the relative frequency of direct hits that were category 4 hurricanes?
- A. 0.0768
- B. 0.0659
- C. 0.2601
- D. Not enough information to calculate
Solution
B
Exercise 24
What is the relative frequency of direct hits that were AT MOST a category 3 storm?
- A. 0.3480
- B. 0.9231
- C. 0.2601
- D. 0.3370
Solution
B
The next three questions refer to the following: A study was done to determine the age, number of times per week and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed.
Exercise 25
‘Number of times per week’ is what type of data?
- A. qualitative
- B. quantitative - discrete
- C. quantitative - continuous
Solution
B
Exercise 26
The sampling method was:
- A. simple random
- B. systematic
- C. stratified
- D. cluster
Solution
B
Exercise 27
‘Duration (amount of time)’ is what type of data?
- A. qualitative
- B. quantitative - discrete
- C. quantitative - continuous
Solution
C
Exercise 28
Name the sampling method used in each of the following situations:
- a. A woman in the airport is handing out questionnaires to travelers asking them to evaluate the airport’s service. She does not ask travelers who are hurrying through the airport with their hands full of luggage, but instead asks all travelers sitting near gates and who are not taking naps while they wait.
- b. A teacher wants to know if her students are doing homework so she randomly selects rows 2 and 5, and then calls on all students in row 2 and all students in row 5 to present the solution to homework problems to the class.
- c. The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out which asks for information about age, as well as about other variables of interest.
- d. The librarian at a public library wants to determine what proportion of the library users are children. The librarian has a tally sheet on which she marks whether the books are checked out by an adult or a child. She records this data for every 4th patron who checks out books.
- e. A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate, the party’s polling staff calls 1200 randomly selected phone numbers. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked who he/she intends to vote for and whether the debate changed his/her opinion of the candidates.
Solution
- a. Convenience
- b. Cluster
- c. Stratified
- d. Systematic
- e. Simple Random
Exercise 29
Several online textbook retailers advertise that they have lower prices than on-campus bookstores. However, an important factor is whether the internet retailers actually have the textbooks that students need in stock. Students need to be able to get textbooks promptly at the beginning of the college term. If the book is not available, then a student would not be able to get the textbook at all, or might get a delayed delivery if the book is back ordered.
A college newspaper reporter is investigating textbook availability at online retailers. He decides to investigate one textbook for each of the following 7 subjects: calculus, biology, chemistry, physics, statistics, geology, and general engineering. He consults textbook industry sales data and selects the most popular nationally used textbook in each of these subjects. He visits websites for a random sample of major online textbook sellers and looks up each of these 7 textbooks to see if they are available in stock for quick delivery through these retailers. Based on his investigation, he writes an article in which he draws conclusions about the overall availability of all college textbooks through online textbook retailers.
Write an analysis of his study that addresses the following issues: Is his sample representative of the population of all college textbooks? Explain why or why not. Describe some possible sources of bias in this study, and how it might affect the results of the study. Give some suggestions about what could be done to improve the study.
Solution
The answer below contains some of the issues that students might discuss for this problem. Individual student's answers may also identify other issues that pertain to this problem that are not included in the answer below.
The sample is not representative of the population of all college textbooks. Two reasons why it is not representative are that he only sampled 7 subjects and he only investigated one textbook in each subject.
There are several possible sources of bias in the study. The 7 subjects that he investigated are all in mathematics and the sciences; there are many subjects in the humanities, social sciences, and many other subject areas, (for example: literature, art, history, psychology, sociology, business) that he did not investigate at all. It may be that different subject areas exhibit different patterns of textbook availability, but his sample would not detect such results. He also only looked at the most popular textbook in each of the subjects he investigated. The availability of the most popular textbooks may differ from the availability of other textbooks in one of two ways: (a) the most popular textbooks may be more readily available online, because more new copies are printed and more students nationwide selling back their used copies OR (b) the most popular textbooks may be harder to find available online, because more student demand exhausts the supply more quickly. In reality, many college students do not use the most popular textbook in their subject, and this study gives no useful information about the situation for those less popular textbooks.
He could improve this study by (a) expanding the selection of subjects he investigates so that it is more representative of all subjects studied by college students and (b) expanding the selection of textbooks he investigates within each subject to include a mixed representation of both the popular and less popular textbooks.