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Chapter 4: Q 37. (page 230)

The Web portal AOL places opinion poll questions next to many of its news stories. Simply click your response to join the sample. One of the questions

in January 2008 was “Do you plan to diet this year?” More than 30,000 people responded, with 68% saying “Yes.” You can conclude that

(a) about 68% of Americans planned to diet in 2008

(b) the poll used a convenience sample, so the results tell us little about the population of all adults.

(c) the poll uses voluntary response, so the results tell us little about the population of all adults.

(d) the sample is too small to draw any conclusion.

(e) None of these.

Short Answer

Expert verified

The correct option is (c).

Step by step solution

01

Given information

More than 30,000 people responded, with 68 percent indicating that they had planned their diet for the year.

02

Concept

A simple random sample (SRS) of size n is made up of n people chosen from the population with an equal chance of being the sample that is actually chosen.

03

Explanation

The participant is given the option of clicking an answer, which results in a voluntary response. As a result, there is the potential for a voluntary response bias. As a result of the poll's use of voluntary responses, the data reveal little about the adult population.

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Most popular questions from this chapter

An example of a non-sampling error that can reduce the accuracy of a sample survey is

(a) using voluntary response to choose the sample.

(b) using the telephone directory as the sampling frame.

(c) interviewing people at shopping malls to obtain a sample.

(d) variation due to chance in choosing a sample at random.

(e) inability to contact many members of the sample.

Do reducing diets work? Dr. Linda Stern and her colleagues recruited 132obese adults at the Philadelphia Veterans Affairs Medical Center in Pennsylvania. Half of the participants were randomly assigned to a low-carbohydrate diet and the other half were assigned to a low-fat diet. Researchers measured each participant’s change in weight and cholesterol level after six months and again after one year. Subjects in the low-carb diet group lost significantly more weight than subjects in the low-fat diet group during the first six months of the study. At the end of a year, however, the average weight loss for subjects in the two groups was not significantly different.

(a) Why did researchers randomly assign the subjects to the diet treatments?

(b) Explain to someone who knows little statistics what “lost significantly more weight” means.

(c) The subjects in the low-carb diet group lost an aver-age of 5.1kg in a year. The subjects in the low-fat diet group lost an average of 3.1kg. Explain how this infor-

mation could be consistent with the fact that weight loss in the two groups was not significantly different.

Each of the following is a source of error in a sample survey. Label each as sampling error or non sampling error, and explain your answers.

(a) The telephone directory is used as a sampling frame.

(b) The person cannot be contacted in five calls.

(c) Interviewers choose people walking by on the sidewalk to interview.

2. A survey paid for by makers of disposable diapers found that 84% of the sample opposed banning disposable diapers. Here is the actual question:

Sleep debt (3.2)A researcher reported that the average teenager needs 9.3 hours of sleep per night but gets only 6.3hours.17By the end of a 5-day school week, a teenager would accumulate about 15 hours of “sleep debt.” Students in a high school statistics class were skeptical, so they gathered data on the amount of sleep debt (in hours) accumulated over time (in days) by a random sample of 25high school students. The resulting least-squares regression equation for their data is Sleepdebt⏜=2.23+3.17(days). Do the students have reason to be skeptical of the research study’s reported results? Explain.

Sampling the forest To gather data on a 1200-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of 1410 equally spaced circular plots over a map

of the forest. A ground survey visited a sample of 10% of these plots.12

(a) Explain how you would use technology or Table D to choose an SRS of 141 plots. Your description should be clear enough for a classmate to obtain your results.

(b) Use your method from (a) to choose the first 3 plots.
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