## Sampling and Data Homework

Solve these problems, then check your answers against the given solutions.

### Exercises

##### Exercise 1

For each item below:

- i. Identify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) that would be used to describe a response.
- ii. Give an example of the data.

- Number of tickets sold to a concert
- Amount of body fat
- Favorite baseball team
- Time in line to buy groceries
- Number of students enrolled at Evergreen Valley College
- Most-watched television show
- Brand of toothpaste
- Distance to the closest movie theater
- Age of executives in Fortune 500 companies
- Number of competing computer spreadsheet software packages

##### Exercise 2

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 Frequency for Adults with Gum Disease

# Flossing per Week | Frequency | Relative Frequency | Cumulative Relative Freq. |
---|---|---|---|

0 | 27 | 0.4500 | |

1 | 18 | ||

3 | 0.9333 | ||

6 | 3 | 0.0500 | |

7 | 1 | 0.0167 |

Table 1.2

- Fill in the blanks in the table above.
- What percent of adults flossed six times per week?
- What percent flossed at most three times per week?

##### Exercise 3

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.

- Population
- Sample
- Parameter
- Statistic
- Variable
- Data

##### Exercise 4

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.

- Population
- Sample
- Parameter
- Statistic
- Variable
- Data

##### Exercise 5

A marriage counselor is interested in the proportion the clients she counsels that stay married. Define the following in terms of the study. Give examples where appropriate.

- Population
- Sample
- Parameter
- Statistic
- Variable
- Data

##### Exercise 6

A marketing company is interested in the proportion of people that will buy a particular product. Define the following in terms of the study. Give examples where appropriate.

- Population
- Sample
- Parameter
- Statistic
- Variable
- Data

##### Exercise 7

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. The results of this survey are listed in the table below.

Reasons for Taking LBCC Distance Learning Courses

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% |

I like computer technology |
52.1% |

Thought DE would be more varied and interesting |
53.2% |

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.

- Why can the percents add up to over 100%?
- Does that necessarily imply a mistake in the report?
- How do you think the question was worded to get responses that totaled over 100%?
- How might the question be worded to get responses that totaled 100%?

##### Exercise 8

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?

- All Lake Tahoe Community College students
- All Lake Tahoe Community College English students
- All Lake Tahoe Community College students in her classes
- All Lake Tahoe Community College math students

##### Exercise 9

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

Frequency of Hurricane Direct Hits

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 |

- 0.0768
- 0.0659
- 0.2601
- Not enough information to calculate

##### Exercise 10

Name the sampling method used in each of the following situations:

- 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.
- 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.
- 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.
- 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.
- 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.

Source: Barbara Illowsky and Susan Dean, https://archive.org/details/CollaborativeStatisticsHomeworkBook/page/n16/mode/1up

This work is licensed under a Creative Commons Attribution 4.0 License.