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A $2008$New York Times article on public opinion about steroid use in baseball discussed the results of a sample survey. The survey found that $34\%$of adults think that at least half of Major League Baseball (MLB) players 鈥渦se steroids to enhance their athletic performance.鈥� Another $36\%$thought that about a quarter of MLB players uses steroids; $8\%$had no opinion. Here is part of the Times鈥� statement on 鈥淗ow the Poll Was Conducted鈥�: The latest New York Times/CBS News Poll is based on telephone interviews conducted March $15$

through March 1$8$with $1,067$adults throughout the United States.鈥� The sample of telephone numbers called was randomly selected by a computer from a list of more than $42,000$active residential exchanges across the country. The exchanges were chosen to ensure that each region of the country was represented in proportion to its population. In each exchange, random digits were added to form a complete telephone number, thus permitting access to listed and unlisted numbers. In each household, one adult was designated by a random procedure to be the respondent for the survey.

(a) Explain why the sampling method used in this survey was not a simple random sample.

(b) Why was one adult chosen at random in each household to respond to the survey?

(c) Explain how undercover could lead to bias in this sample survey.

Step by step solution

01

Part (a) Step 1: Given information

According to the report, $34\%$ of individuals believe that MLB players utilise steroid to improve their performance.

02

Part (a) Step 2: Concept

The random assignment method assigns subjects to treatments based on chance. Before the treatments are applied, random assignment establishes treatment groups that are comparable (except for chance variance). In experiments, randomization and comparison combined prevent bias or systematic favoritism.

03

Part (a) Step 3: Explanation

According to the report, $34\%$ of individuals believe that MLB players utilize steroids to improve their performance. Furthermore, $36\%$ of adults believe that players utilize steroids, while the remaining $80\%$ have no view. Because the poll does not include persons who do not have access to a telephone, it is not a simple random sample. The sampling procedure is not a simple random sample because not everyone has the same chance of being chosen.

04

Part (b) Step 1: Explanation

If the call is made, there is a chance that a few adults will pick up the phone more frequently than others, and there will be differences in opinions.

05

Part (c) Step 1: Explanation

Because they do not have telephones for all of the participants, they were unable to include them in the survey. As a result, a huge percentage of the population was overlooked, perhaps leading to bias.

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