Ch. 7 - Estimating Parameters and Determining Sample Sizes

Triola - Elementary Statistics 14th Edition

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Triola 14th Edition

Ch. 7 - Estimating Parameters and Determining Sample Sizes

Problem 7.3a

Chapter 7, Problem 7.3a

Voting Survey In a survey of 1002 people, 70% said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote.

a. Among the 1002 people surveyed, what is the actual number of people who said that they voted?

Verified step by step guidance

Step 1: Identify the total number of people surveyed, which is given as 1002.

Step 2: Note that 70% of the surveyed people said they voted. Convert this percentage to a decimal by dividing by 100, which gives 0.70.

Step 3: To find the actual number of people who said they voted, multiply the total number of surveyed people (1002) by the decimal representation of the percentage (0.70).

Step 4: Use the formula: \( \text{Number of people who said they voted} = 1002 \times 0.70 \).

Step 5: Perform the multiplication to determine the result, which represents the number of people who claimed they voted in the survey.

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Key Concepts

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

Percentage Calculation

Percentage calculation is a mathematical process used to determine a portion of a whole. In this context, to find the actual number of people who said they voted, you multiply the total number of surveyed individuals (1002) by the percentage of those who claimed to have voted (70%). This results in a straightforward calculation that helps quantify survey responses.

Survey Sampling

Survey sampling involves selecting a subset of individuals from a larger population to estimate characteristics of the whole group. In this case, the 1002 surveyed individuals represent a sample from the broader population of eligible voters. Understanding sampling is crucial for interpreting survey results and assessing their reliability and validity.

Voter Turnout

Voter turnout refers to the percentage of eligible voters who actually cast a ballot in an election. The survey indicates that 70% of respondents claimed to have voted, while official records show that only 61% of eligible voters participated. This discrepancy highlights the importance of distinguishing between self-reported voting behavior and actual voting records, which can inform discussions about electoral engagement.

Related Practice

Textbook Question

Controversial Song The song “Baby It’s Cold Outside” generated much controversy because of its lyrics and tone. CBS New York conducted a survey by asking viewers to use the Internet to respond to a question asking whether that song was really too offensive to play. Among 1043 Internet users who chose to respond, 986 said that the song was not too offensive, and 57 of the respondents said that the song was too offensive.

a. Construct a 95% confidence interval estimate of the proportion of the population having the belief that the song is not too offensive.

Textbook Question

Space Mountain Use the following wait times (minutes) for the Space Mountain ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B). Construct a 95% confidence interval estimate of the mean of all wait times. Write a brief statement that interprets that confidence interval.

40 35 40 40 25 80 50 30 35 40

Textbook Question

Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

Job Interviews In a Harris poll of 514 human resource professionals, 45.9% said that body piercings and tattoos were big personal grooming red flags.

a. Among the 514 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big personal grooming red flags?

Textbook Question

Airline Seating You are the operations manager for American Airlines and you are considering a higher fare level for passengers in aisle seats. You want to estimate the percentage of passengers who now prefer aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 95% confident that the sample percentage is within 2.5 percentage points of the true population percentage.

a. Assume that nothing is known about the percentage of passengers who prefer aisle seats.

Textbook Question

Brain Volumes Use these measures of brain volumes from Data Set 12 “IQ and Brain Size” in Appendix B. Use the bootstrap method with 1000 bootstrap samples.

a. Use 1000 bootstrap samples to construct a 90% confidence interval estimate of the population mean.

Textbook Question

Astrology A sociologist plans to conduct a survey to estimate the percentage of adults who believe in astrology. How many people must be surveyed if we want a confidence level of 99% and a margin of error of four percentage points?

a. Assume that nothing is known about the percentage to be estimated.