For Exercises 3.1, 3.2, 3.3 and 3.4, see pages 164–165; for Exercise 3.5, see page 166; for Exercise 3.6, see page 167; for Exercises 3.7, 3.8, and 3.9, see pages 168–169; and for Exercises 3.10 and 3.11, see pages 169–170.
In several of the following exercises, you are asked to identify the type of data that is described. Possible answers include anecdotal data, available data, observational data that are from sample surveys, observational data that are not from sample surveys, and experimental data. It is possible for some data to be classified in more than one category.
3.12 Not enough tuna. You like to eat tuna fish sandwiches. Recently you have noticed that there does not seem to be as much tuna as you expect when you open the can. Identify the type of data that this represents, and describe how it can or cannot be used to reach a conclusion about the amount of tuna in cans of tuna fish. Is this an experiment? If yes, what is the treatment?
3.13 More about tuna. According to a story in Consumer Reports, three major producers of canned tuna agreed to pay $3,300,000 to settle claims in California that the amount of tuna in their cans was less than the amount printed on the label of the cans.6 What kind of data do you think was used in this situation to convince the producers to pay this amount of money to settle the claims? Explain your answer fully.
3.13 The data used was likely observational data from a sample survey. Most likely, a random sample of cans of tuna was measured and compared with the amount printed on the labels.
3.14 What’s wrong? Explain what is wrong in each of the following statements.
(a) Available data is always anecdotal.
(b) A census collects information on a subset of the population of interest.
(c) A sample survey usually involves a treatment.
3.15 Satisfaction with allocation of concert tickets. Your college sponsored a concert that sold out.
(a) After the concert, an article in the student newspaper reported interviews with three students who were unable to get tickets and were very upset. What kind of data does this represent? Explain your answer.
(b) A week later the student organization that sponsored the concert set up a website where students could rank their satisfaction with the way that the tickets were allocated using a 5-point scale with values “very satisfied,” “satisfied,” “neither satisfied nor unsatisfied,” “dissatisfied,” and “very dissatisfied.” The website was open to any students who chose to provide their opinion. How would you classify these data? Give reasons for your answer.
(c) Suppose that the website in part (b) was changed so that only a sample of students from the college were invited by a text message to respond, and those who did not respond within three days were sent an additional text message reminding them to respond. How would your answer to part (b) change, if at all?
(d) Is the description in part (c) an experiment? If yes, what is the treatment?
(e) Write a short summary contrasting different types of data using your answers to parts (a), (b), (c), and (d) of this exercise.
3.15 (a) This is a sample survey if it is supposed to represent only those who did not get tickets; otherwise, it is anecdotal evidence and certainly doesn’t apply to all of those who tried to get tickets to the concert. (b) This represents a sample survey of all those that tried to get tickets to the concert. (c) This also represents a sample survey of all those who tried to get tickets to the concert. It differs from part (b) because only a sample of students were selected to participate rather than allowing participants to be self-selected. (d) It is not an experiment, there is no treatment. (e) The method used in part (a) is not very useful, especially if it was determined they were upset before being interviewed. The method in part (b) also can be problematic because those who choose to respond may have strong opinions, especially negative ones. The method in part (c) is likely the best of the three in order to get an accurate representation of students’ opinion on how the tickets were allocated.
3.16 Does echinacea reduce the severity of the common cold? In a study designed to evaluate the benefits of taking echinacea when you have a cold, 719 patients were randomly divided into four groups. The groups were (1) no pills, (2) pills that had no echinacea, (3) pills that had echinacea but the subjects did not know whether or not the pills contained echinacea, and (4) pills that had echinacea and the bottle containing the pills stated that the contents included echinacea. The outcome was a measure of the severity of the cold.7
(a) Identify the type of data collected in this study. Give reasons for your answer.
(b) Is this an experiment? If yes, what is the treatment?