Summary: This module presents students with a number of problems related to statistical sampling and data. In particular, students are asked to demonstrate understanding of concepts such as frequency, relative frequency, and cumulative relative frequency, random samples, quantitative vs. qualitative data, continuous vs. discrete data, and other key terms related to sampling and data.
Note: You are viewing an old version of this document. The latest version is available here.
For each item below:
Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:
| # of Courses | Frequency | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|---|
| 1 | 30 | 0.6 | |
| 2 | 15 | ||
| 3 |
Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below:
| # Flossing per Week | Frequency | Relative Frequency | Cumulative Relative Freq. |
|---|---|---|---|
| 0 | 27 | 0.45 | |
| 1 | 18 | ||
| 3 | 0.93 | ||
| 6 | 3 | 0.05 | |
| 7 | 1 | 0.02 |
A fitness center is interested in the average amount of time a client exercises in the center each week. Define the following in terms of the study. Give examples where appropriate.
Ski resorts are interested in the average age that children take their first ski and snowboard lessons. They need this information to optimally plan their ski classes. Define the following in terms of the study. Give examples where appropriate.
A cardiologist is interested in the average recovery period for her patients who have had heart attacks. Define the following in terms of the study. Give examples where appropriate.
Insurance companies are interested in the average health costs each year for their clients, so that they can determine the costs of health insurance. Define the following in terms of the study. Give examples where appropriate.
A politician is interested in the proportion of voters in his district who think he is doing a good job. Define the following in terms of the study. Give examples where appropriate.
A marriage counselor is interested in the proportion the clients she counsels who stay married. Define the following in terms of the study. Give examples where appropriate.
Political pollsters may be interested in the proportion of people who will vote for a particular cause. Define the following in terms of the study. Give examples where appropriate.
A marketing company is interested in the proportion of people who will buy a particular product. Define the following in terms of the study. Give examples where appropriate.
Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys 6 flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study.
Suppose you want to determine the average number of students per statistics class in your state. Describe a possible sampling method in 3 – 5 complete sentences. Be detailed.
Suppose you want to determine the average number of cans of soda drunk each month by persons in their twenties. Describe a possible sampling method in 3 - 5 complete sentences. Be detailed.
726 distance learning students at Long Beach City College in the 2004-2005 academic year were surveyed and asked the reasons they took a distance learning class. (Source: Amit Schitai, Director of Instructional Technology and Distance Learning, LBCC). The results of this survey are listed in the table below.
| Convenience | 87.6% |
| Unable to come to campus | 85.1% |
| Taking on-campus courses in addition to my DL course | 71.7% |
| Instructor has a good reputation | 69.1% |
| To fulfill requirements for transfer | 60.8% |
| To fulfill requirements for Associate Degree | 53.6% |
| Thought DE would be more varied and interesting | 53.2% |
| I like computer technology | 52.1% |
| Had success with previous DL course | 52.0% |
| On-campus sections were full | 42.1% |
| To fulfill requirements for vocational certification | 27.1% |
| Because of disability | 20.5% |
Assume that the survey allowed students to choose from the responses listed in the table above.
Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows:
2; 5; 7; 2; 2; 10; 20; 15; 0; 7; 0; 20; 5; 12; 15; 12; 4; 5; 10
The following table was produced:
| Data | Frequency | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|---|
| 0 | 2 |
|
0.1053 |
| 2 | 3 |
|
0.2632 |
| 4 | 1 |
|
0.3158 |
| 5 | 3 |
|
0.1579 |
| 7 | 2 |
|
0.5789 |
| 10 | 2 |
|
0.6842 |
| 12 | 2 |
|
0.7895 |
| 15 | 1 |
|
0.8421 |
| 20 | 1 |
|
1.0000 |
A “random survey” was conducted of 3274 people of the “microprocessor generation” (people born since 1971, the year the microprocessor was invented). It was reported that 48% of those individuals surveyed stated that if they had $2000 to spend, they would use it for computer equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users. (Source: San Jose Mercury News)
Additional information: The survey was reported by Intel Corporation of individuals who visited the Los Angeles Convention Center to see the Smithsonian Institure's road show called “America’s Smithsonian.”
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.
What is the population she is interested in?
D
Consider the following:
In this case,
A
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
B
The instructor’s sample produces an average number of days absent of 3.5 days. This value is an example of a
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)
| 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 |
What is the relative frequency of direct hits were category 4 hurricanes?
B
What is the relative frequency of direct hits were AT MOST a category 3 storm?
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.
‘Number of times per week’ is what type of data?
B
The sampling method was:
B
‘Duration (amount of time)’ is what type of data?
C