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Chapter 4: Q. 32 (page 239)

Weight? Wait what? Marcos asked a random sample of 50mall shoppers for their weight. Twenty-five of the shoppers were asked directly and the other 25 were asked anonymously by means of a 鈥渟ecret ballot.鈥� The mean reported weight was13 pounds heavier for the anonymous group. Explain why the two means are so different.

Short Answer

Expert verified

This is because, for personal reasons, people do not want to confess their true weight when they are questioned directly. They don't want other people to know how much they weight.

Step by step solution

01

Given Information

We have to explain why the two means are so different.

02

Simplification

Marcos inquired about the weight of a random sample of 50mall patrons. Two of the groups were split in half. The first half of the group was asked directly about their weight, while the other half was asked anonymously through "secret ballot." As a result, the anonymous group's mean was greater than the group that was personally questioned. This is because, for personal reasons, people do not want to confess their true weight when they are questioned directly. They don't want other people to know how much they weight.

As a result, when they were asked directly, the survey results were skewed since their responses were fake. When they were asked about their weight anonymously, they knew their identity would be kept hidden, so they gave honest answers in the survey. As a result, they are distinct.

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Most popular questions from this chapter

A local news agency conducted a survey about unemployment by randomly dialing phone

numbers during the work day until it gathered responses from 1000 adults in its state. In

the survey, 19% of those who responded said they were not currently employed. In reality,

only 6% of the adults in the state were not currently employed at the time of the survey.

Which of the following best explains the difference in the two percentages?

a. The difference is due to sampling variability. We shouldn鈥檛 expect the results of a

random sample to match the truth about the population every time.

b. The difference is due to response bias. Adults who are employed are likely to lie and

say that they are unemployed.

c. The difference is due to undercoverage bias. The survey included only adults and did

not include teenagers who are eligible to work.

d. The difference is due to nonresponse bias. Adults who are employed are less likely to

be available for the sample than adults who are unemployed.

e. The difference is due to voluntary response. Adults are able to volunteer as a member

of the sample.

How is your room? A hotel has 30floors with 40rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to select 120rooms and survey the registered guest in each of the selected rooms about his or her overall satisfaction with the property.

a. Describe how to obtain a sample of 120rooms using stratified random sampling. Explain your choice of strata and why this method might be preferred to simple random sampling.

b. Describe how to obtain a sample of 120rooms using cluster sampling. Explain your choice of clusters and why this method might be preferred to simple random sampling.

Immigration reform A news organization wants to know what percent of U.S. residents support a 鈥減athway to citizenship鈥� for people who live in the United States illegally. The news organization randomly selects registered voters for the survey. Describe how under coverage might lead to bias in this study. Explain the likely direction of the bias.

Can texting make you healthier? Researchers randomly assigned 700Australian adults

to either receive usual health care or usual heath care plus automated text messages with

positive messages, such as 鈥淲alking is cheap. It can be done almost anywhere. All you

need is comfortable shoes and clothing.鈥� The group that received the text messages

showed a statistically significant increase in physical activity鈥渟tatistically significant鈥� in this context?

a. The results of this study are very important.

b. The results of this study should be generalized to all people.

c. The difference in physical activity for the two groups is greater than 0.

d. The difference in physical activity for the two groups is very large.

e. The difference in physical activity for the two groups is larger than the difference

that could be expected to happen by chance alone.

A popular website places opinion poll questions next to many of its news stories. Simply

click your response to join the sample. One of the questions was 鈥淒o you plan to diet this

year?鈥� More than 30,000 people responded, with 68% saying 鈥淵es.鈥� Which of the

following is true?

a. About 68% of Americans planned to diet.

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.
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