Homework

For each of the following situations, indicate whether it would be best modeled with a mathematical model or a statistical model. Explain your answers.

1. driving time from New York to Florida
2. departure time of a commuter train at rush hour
3. distance from your house to school
4. temperature of a refrigerator at any given time
5. weight of a bag of rice at the store

Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally.

Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance.

A marriage counselor is interested in the proportion of clients she counsels who stay married.

A marketing company is interested in the proportion of people who will buy a particular product.

Consider the following

$X$ = number of days a Lake Tahoe Community College math student is absent.

In this case, X is an example of which of the following?

1. variable
2. population
3. statistic
4. data

number of tickets sold to a concert

favorite baseball team

number of students enrolled at Evergreen Valley College

brand of toothpaste

age of executives in Fortune 500 companies

Number of times per week is what type of data?

1. qualitative
2. quantitative discrete
3. quantitative continuous

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 six 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.

1. Using complete sentences, list three things wrong with the way the survey was conducted.
2. Using complete sentences, list three ways that you would improve the survey if it were to be repeated.

Suppose you want to determine the mean number of cans of soda drunk each month by students in their twenties at your school. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

List some practical difficulties involved in getting accurate results from a mailed survey.

The instructor takes her sample by gathering data on five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is which of the following?

1. cluster sampling
2. stratified sampling
3. simple random sampling
4. convenience sampling

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

1. 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 who are sitting near gates and not taking naps while they wait.
2. A teacher wants to know if her students are doing homework, so she randomly selects rows two and five and then calls on all students in row two and all students in row five to present the solutions to homework problems to the class.
3. 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 asking for information about age, as well as about other variables of interest.
4. 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 books are checked out by an adult or a child. She records this data for every fourth patron who checks out books.
5. 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 1,200 randomly selected phone numbers. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked whom he or she intends to vote for and whether the debate changed his or her opinion of the candidates.

The Well-Being Index is a survey that follows trends of U.S. residents on a regular basis. There are six areas of health and wellness covered in the survey: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment, and Basic Access. Some of the questions used to measure the Index are listed below.

Identify the type of data obtained from each question used in this survey: qualitative, quantitative discrete, or quantitative continuous.

1. Do you have any health problems that prevent you from doing any of the things people your age can normally do?
2. During the past 30 days, for about how many days did poor health keep you from doing your usual activities?
3. In the last seven days, on how many days did you exercise for 30 minutes or more?
4. Do you have health insurance coverage?

Crime-related and demographic statistics for 47 US states in 1960 were collected from government agencies, including the FBI's Uniform Crime Report. One analysis of this data found a strong connection between education and crime indicating that higher levels of education in a community correspond to higher crime rates.

Which of the potential problems with samples discussed in Data, Sampling, and Variation in Data and Sampling could explain this connection?

A scholarly article about response rates begins with the following quote:

“Declining contact and cooperation rates in random digit dial (RDD) national telephone surveys raise serious concerns about the validity of estimates drawn from such research.”⁶

The Pew Research Center for People and the Press admits

“The percentage of people we interview—out of all we try to interview—has been declining over the past decade or more.”⁷

1. What are some reasons for the decline in response rate over the past decade?
2. Explain why researchers are concerned with the impact of the declining response rate on public opinion polls.

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in Table 1.38.

1. Fill in the blanks in Table 1.38.
2. What percent of adults flossed six times per week?
3. What percent flossed at most three times per week?

How much time does it take to travel to work? Table 1.40 shows the mean commute time by state for workers at least 16 years old who are not working at home. Find the mean travel time, and round off the answer properly.

What is the relative frequency of direct hits that were category 4 hurricanes?

1. .0768
2. .0659
3. .2601
4. not enough information to calculate

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

Use key terms from this module to describe the design of this experiment.

The graph in Figure 1.15 shows the number of complaints for six different airlines as reported to the U.S. Department of Transportation in February 2013. Alaska, Pinnacle, and Airtran Airlines have far fewer complaints reported than American, Delta, and United. Can we conclude that American, Delta, and United are the worst airline carriers since they have the most complaints?

Figure 1.15

An epidemiologist is studying the spread of the common cold among college students. He is interested in how the temperature of the dorm room correlates with the incidence of new infections. How can he design an observational study to answer this question? If he chooses to use surveys in his measurements, what type of questions should he include in the survey?