Ch. 1 - Introduction to Statistics

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 1 - Introduction to Statistics

Problem 1.1.30

Chapter 1, Problem 1.1.30

In Exercises 29–36, identify what is wrong.
Healthy Water In a USA Today online poll, 951 Internet users chose to respond, and 57% of them said that they prefer drinking bottled water instead of tap water.

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Identify the type of sampling method used in the poll. In this case, the poll was conducted online, and participants chose to respond voluntarily.

Understand the concept of voluntary response sampling. This method often leads to biased results because it tends to attract individuals who have strong opinions, which may not represent the general population.

Consider the potential for selection bias. Since the poll was conducted online, it only includes responses from Internet users, excluding those without Internet access or those who did not see the poll.

Evaluate the sample size and its representativeness. Although 951 responses might seem substantial, the sample is not randomly selected, which affects its ability to accurately reflect the preferences of the broader population.

Reflect on the implications of the findings. The 57% figure may not be reliable for making generalizations about the entire population's preference for bottled water over tap water due to the non-random sampling method used.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sampling Bias

Sampling bias occurs when the sample is not representative of the population. In this case, the poll was conducted online, and only those who chose to respond were included, which may not reflect the views of the general population. This self-selection can lead to biased results, as it might over-represent individuals with strong opinions about bottled water.

Voluntary Response Sample

A voluntary response sample is a type of non-probability sampling where participants self-select into the survey. This method often leads to biased outcomes because individuals with strong opinions are more likely to participate. In the given poll, the 951 Internet users who responded may not accurately represent the broader population's preferences regarding bottled water.

Generalizability

Generalizability refers to the extent to which findings from a sample can be applied to the larger population. Due to the non-random nature of the sample in the poll, the results cannot be reliably generalized to all people. The lack of random sampling and potential biases mean that the 57% figure may not accurately reflect the true preference of the entire population.

Related Practice

Textbook Question

In Exercises 21–28, determine whether the study is an experiment or an observational study, and then identify a major problem with the study.

Sleep Study When designing the study of a new treatment for insomnia in adults, researchers were criticized because their test subjects consisted of 75 college students. They then expanded the study so that 750 college students were given the treatment.

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Textbook Question

In Exercises 37–44, answer the given questions, which are related to percentages.

Percentages in Advertising An ad for Big Skinny wallets included the statement that one of their wallets “reduces your filled wallet size by 50%–200%.” What is wrong with this statement?

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Textbook Question

In Exercises 13–20, determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.

Bias in Jury Selection In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty, and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry.

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Textbook Question

In Exercises 9–20, identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster.

Cormorant Density Cormorant bird population densities were studied by using the “line transect method” with aircraft observers flying along the shoreline of Lake Huron and collecting sample data at intervals of every 20 km (based on data from Journal of Great Lakes Research).

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Textbook Question

In Exercises 37–44, answer the given questions, which are related to percentages.

Workplace Attire In a survey conducted by Opinion Research Corporation, 1000 adults were asked to identify “what is inappropriate in the workplace.” Of the 1000 subjects, 70% said that miniskirts were not appropriate in the workplace.

b. Among the 1000 respondents, 550 said that shorts are unacceptable in the workplace. What percentage of respondents said that shorts are unacceptable in the workplace?

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Textbook Question

In Exercises 21–28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) best describes the given data.

Areas of States A data set consists of the areas of each of the 50 United States.

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In Exercises 29–36, identify what is wrong.Healthy Water In a USA Today online poll, 951 Internet users chose to respond, and 57% of them said that they prefer drinking bottled water instead of tap water.

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Key Concepts

Sampling Bias

Voluntary Response Sample

Generalizability

In Exercises 29–36, identify what is wrong.
Healthy Water In a USA Today online poll, 951 Internet users chose to respond, and 57% of them said that they prefer drinking bottled water instead of tap water.