Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 9.2, Problem 32E
Based on survey of a representative sample of 1000 adult Americans, YouGov estimated that the proportion of adult Americans who have less than $1000 in savings is 0.430 (“People More Likely to Save with an Opt-Out System,” today.yougov.com/news/2016/04/25/savings/). The margin of error for a 95% confidence level associated with this estimate is 0.03. Show how this margin of error was calculated.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
During the recovery from the Great Recession of 2007-2009, the economic situation for many families improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national level. To estimate the national average of the percent of low-income working families, a representative simple random sample of the percent of low-income working families from each of the country’s reporting jurisdictions could be used to calculate a point estimate and create a related confidence interval. With this confidence interval a better picture of the nation’s recovery can be had and legislative decisions can be made.
Describe in two or three sentences how a simple random sample of size n=20 could be obtained from the full list of jurisdictions provided for use with this assignment.
A researcher reported that a sample of size n=30 produced a sample mean of 32.56% and a sample standard deviation of 6.56%. Use this information to calculate a 90%…
During the recovery from the Great Recession of 2007-2009, the economic situation for many families improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national level. To estimate the national average of the percent of low-income working families, a representative simple random sample of the percent of low-income working families from each of the country’s reporting jurisdictions could be used to calculate a point estimate and create a related confidence interval. With this confidence interval a better picture of the nation’s recovery can be had and legislative decisions can be made.
If a limited amount of federal funds have been allocated to assist jurisdictions whose “percent of low-income working families” exceeds a threshold based on the upper limit of a confidence interval, what would be the effect of using a confidence level that is higher than 90%?
If a public official requests funds based on a confidence…
During the recovery from the Great Recession of 2007-2009, the economic situation for many families improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national level. To estimate the national average of the percent of low-income working families, a representative simple random sample of the percent of low-income working families from each of the country’s reporting jurisdictions could be used to calculate a point estimate and create a related confidence interval. With this confidence interval a better picture of the nation’s recovery can be had and legislative decisions can be made.
6. Describe in two or three sentences how a simple random sample of size n=20 could be obtained from the full list of jurisdictions provided for use with this assignment.
7. A researcher reported that a sample of size n=30 produced a sample mean of 32.56% and a sample standard deviation of 6.56%. Use this information to calculate a 90% confidence…
Chapter 9 Solutions
Introduction To Statistics And Data Analysis
Ch. 9.1 - Three different statistics are being considered...Ch. 9.1 - a. Why is an unbiased statistic generally...Ch. 9.1 - The report The 2016 Consumer Financial Literacy...Ch. 9.1 - The authors of the paper Influence of Biofeedback...Ch. 9.1 - Each person in a random sample of 20 students at a...Ch. 9.1 - Suppose that each of 935 smokers received a...Ch. 9.1 - Given below are the sodium contents (in mg) for...Ch. 9.1 - A random sample of n = 12 four-year-old red pine...Ch. 9.1 - A random sample of 10 houses heated with natural...Ch. 9.2 - Explain which would result in a wider large-sample...
Ch. 9.2 - Explain which would result in a wider large-sample...Ch. 9.2 - The formula used to calculate a large-sample...Ch. 9.2 - The use of the interval p(zcriticalvalue)p(1p)n...Ch. 9.2 - For each of the following combinations of sample...Ch. 9.2 - Discuss how each of the following factors affects...Ch. 9.2 - The USA TODAY Snapshot titled Social Media...Ch. 9.2 - Based on data from a survey of 1200 randomly...Ch. 9.2 - The report Parents, Teens and Digital Monitoring...Ch. 9.2 - If a hurricane was headed your way, would you...Ch. 9.2 - The USA TODAY Snapshot titled Big Bang Theory (USA...Ch. 9.2 - The article Most Dog Owners Take More Pictures of...Ch. 9.2 - The Princeton Review 2016 College Hopes and...Ch. 9.2 - The USA TODAY Snapshot titled Babys First Photo...Ch. 9.2 - The report Job Seeker Nation Study...Ch. 9.2 - USA TODAY reported that the proportion of...Ch. 9.2 - The USA TODAY Snapshot titled Have a Nice Trip...Ch. 9.2 - Business Insider reported that a study...Ch. 9.2 - In 2010, the National Football League adopted new...Ch. 9.2 - The article Most Americans Dont Understand the...Ch. 9.2 - The Gallup Organization conducts an annual survey...Ch. 9.2 - The article Hospitals Dispute Medtronic Data on...Ch. 9.2 - Based on survey of a representative sample of 1000...Ch. 9.2 - A discussion of digital ethics appears in the...Ch. 9.2 - In spite of the potential safety hazards, some...Ch. 9.2 - In 2010, the online security firm Symantec...Ch. 9.3 - Given a variable that has at distribution with the...Ch. 9.3 - The formula used to calculate a confidence...Ch. 9.3 - USA TODAY reported that the average amount of...Ch. 9.3 - Samples of two different models of cars were...Ch. 9.3 - USA TODAY reported that the average amount of...Ch. 9.3 - The paper The Effects of Adolescent Volunteer...Ch. 9.3 - Medical research has shown that repeated wrist...Ch. 9.3 - Students in a representative sample of 65...Ch. 9.3 - The paper referenced in the previous exercise also...Ch. 9.3 - Suppose that a random sample of 50 bottles of a...Ch. 9.3 - The authors of the paper Driving Performance While...Ch. 9.3 - The article The Association Between Television...Ch. 9.3 - The paper Patterns and Composition of Weight...Ch. 9.3 - Because of safety considerations, in May 2003 the...Ch. 9.3 - Example 9.3 gave the following airborne times (in...Ch. 9.3 - Consumer Reports gave the following mileage...Ch. 9.3 - Five students visiting the student health center...Ch. 9.3 - The Bureau of Alcohol, Tobacco, and Firearms...Ch. 9.3 - The formula described in this section for...Ch. 9.4 - The following quote is from the article Credit...Ch. 9.4 - Authors of the news release titled Major Gaps...Ch. 9.4 - The paper The Curious Promiscuity of Queen Honey...Ch. 9.5 - A survey on SodaHead...Ch. 9.5 - Prob. 59ECh. 9.5 - Prob. 60ECh. 9.5 - Prob. 61ECh. 9.5 - Prob. 62ECh. 9.5 - Prob. 63ECh. 9.5 - Prob. 64ECh. 9.5 - Prob. 65ECh. 9.6 - Prob. 66ECh. 9.6 - Prob. 67ECh. 9.6 - Teams in the National Football League (NFL) are...Ch. 9.6 - Prob. 69ECh. 9.6 - The Economist collects data each year on the price...Ch. 9.6 - Major League Baseball (MLB) includes two groups of...Ch. 9 - The article Write It by Hand to Make It Stick...Ch. 9 - Prob. 73CRCh. 9 - The report The 2016 Consumer Financial Literacy...Ch. 9 - The report The Politics of Climate (Pew Research...Ch. 9 - The report referenced in the previous exercise...Ch. 9 - Data from a survey of a representative sample was...Ch. 9 - A manufacturer of small appliances purchases...Ch. 9 - A manufacturer of college textbooks is interested...Ch. 9 - The confidence intervals presented in this chapter...Ch. 9 - Prob. 81CRCh. 9 - The interval from 2.33 to 1.75 captures an area of...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- A Gallup Poll in December 2019 reported that 46% of the 5120 adults aged 18 and older in the sample said both their mental and their physical health was good or excellent. Gallup announced, "For results based on the combined sample of 5120 adults, aged 18 and older ... the margin of sampling error is 2 percentage points at the 95% confidence level." Confidence intervals for a percentage follow the form estimate±margin of error Based on the information from Gallup, what is the 95% confidence interval for the percentage of all adults aged 18 and older who would say both their mental and physical health was good or excellent? Give your answer as an interval in the form (lower bound, upper bound). Give your numbers as percentages and as whole numbers. confidence interval: $$ What does it mean to have 95% confidence in this interval? A confidence of 95% in the interval means that 95% of all samples of the same size give an interval that contains the actual…arrow_forwardThe Malayo Colleges Mindanao recently conducted a study analyzing the privacy management habits of teen internet users. In a group of 157 teens, 52 reported having more than 100 followers on Twitter. Find the margin of error of a 90% confidence interval for the true proportion of teens who would report having more than 100 followers on Twitter. Note: Write your answers in decimal form and round it to 4 decimal places.arrow_forwardThe first day of baseball comes in late March, ending in October with the World Series. Does fan support grow as the season goes on? Two CNN/USA Today/Gallup polls, one concluded in March and one in November, both involve random samples of 1001 adults aged 18 and older. In March sample, 45% of the adults claimed to be fans of professional baseball while 51% of the adults in the November sample claimed to be fans. Construct a 99% confidence interval for the difference in the proportion of adults who claim to be fans in March versus November.arrow_forward
- In 2013, the Pew Research Foundation reported that “45% of U.S. adults report that they live with one or more chronic conditions”.11 However, this value was based on a sample, so it may not be a perfect estimate for the population parameter of interest on its own. The study reported a standard error of about 1.2%, and a normal model may reasonably be used in this setting. Create a 95% confidence interval for the proportion of U.S. adults who live with one or more chronic conditions. Also interpret the confidence interval in the context of the study.arrow_forwardMedical professionals at a student health center are trying to alert the undergraduate population about the importance of getting sufficient sleep and the role this plays in their academic performance. The health center staff would like to estimate the true average amount of sleep that the undergraduate students are receiving and construct a 90% confidence interval for this estimate. Furthermore, in order to be useful, the interval can be no more than 1.6 hours WIDE ( so Margin or Error would be half of that). Table 1 reports the results from a pilot test that measured the amount of sleep obtained in a random sampling of undergraduate students. Use the standard deviation from this pilot study as your estimate for the population standard deviation.Table 1: Descriptive statistics for the sleep study Variable mean Std.Dev Hours of sleep 3.25 8.50 Based on the student health department's criteria, the number of students that should be selected is:arrow_forwardA random sample of 300 of toy trains produced by a company are selected from a production line and 60 are found to be defective. Provide a 95% confidence interval estimate of the proportion of all toy trains produced by the company that will be defective. What is the value for the margin of error?arrow_forward
- The Centers for Disease Control and Prevention reported a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have the disease.arrow_forwardAccording to Franchise business review, over 50% of all food franchises earn a profit ofless than $50,000 a year. In a sample of 142 casual dining restaurants, 81 earned a profitof less than $50,000 last year.a. What is the point estimate of the proportion of casual dining restaurants that earned aprofit of less than $50,000 last year?b. Determine the margin of error and provide a 95% confidence interval for theproportion of casual dining restaurants that earned a profit of less than $50,000last year.c. How large a sample is needed if the desired margin of error is .03?arrow_forwardResults from the National Health and Nutrition Examination Survey (NHANES) conducted thirty years ago revealed that out of 378 randomly selected adults in the United States 57 were considered to be obese. In this year’s National Health and Nutrition Examination Survey, out of 426randomly selected adults in the United States 135 were considered to be obese. Use the results of the National Health and Nutrition Examination Survey and a 99% confidence interval to estimate the difference between the percentages of adults in the United States that are obese this year and thirty years ago. Express the estimate both symbolically and verbally.arrow_forward
- There is no prior information about the proportion of Americans who support free trade in 2018. If we want to estimate a 97.5% confidence interval for the true proportion of Americans who support free trade in 2018 with a 0.16 margin of error, how many randomly selected Americans must be surveyed?arrow_forwardIn a random sample of 1,250 adult drivers, 450 said they would cut their driving by 10 percent is this significantly helped the environment. Find a 95 percent confidence interval estimate of the proportion os adult drivers who are willing to cut their driving by 10 percent to help the enviroment.arrow_forwardA drug manufacturer conducted a study to try to determine if theproportion of elderly patients that experienced side effects was differentthan the proportion of younger adults that experienced side effects. Afterconducting the experiment, they computed a 95% confidence interval forthe difference of proportions (elderly less younger adults) was (.135, .228).Based on these results, can they conclude that there is a differencebetween the two groups? Explain why.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License