Elementary Statistics: Picturing the World (7th Edition)
7th Edition
ISBN: 9780134683416
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Textbook Question
Chapter 6.3, Problem 23E
In Exercise 17(b), would a
17. Congress You wish to estimate, with 95% confidence, the population proportion of U.S. adults who think Congress is doing a good or excellent job. Your estimate must be accurate within 4% of the population proportion.
- (a) No preliminary estimate is available. Find the minimum sample size needed.
- (b) Find the minimum sample size needed, using a prior survey that found that 25% of U.S. adults think Congress is doing a good or excellent job. (Source: Rasmussen Reports)
- (c) Compare the results from parts (a) and (b).
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Suppose you would like to estimate, with 97% confidence, the proportion of computers that need repairs or have problems by the time the product is three years old. Your estimate must be accurate within 3.5% of the true proportion.
a. If no preliminary estimate is available, find the minimum sample size needed.
b. Find the minimum sample size needed, using a prior study that found that 19% of computers needed repairs or had problems by the time the product was three years old.c. Compare the results in a) and b) above.
A sociologist wishes to conduct a poll to estimate the percentage of Americans who favor affirmative action programs for women and minorities for admission to college and universities. She wants to use a 2003 estimate of 55% obtained from a Gallup Youth Survey as a prior estimate. What sample size should be obtained if she wishes the estimate to be within 4 percentage points with 90% confidence?
(a) What is the minimum sample size needed assuming that no prior information is available?
(b) What is the minimum sample size needed using a prior study that found that 32% of the respondents said they think Congress is doing a good or excellent job?
(c) How do the results from (a) and (b) compare?
A. Having an estimate of the population proportion reduces the minimum sample size needed.
B. Having an estimate of the population proportion has no effect on the minimum sample size needed.
C. Having an estimate of the population proportion raises the minimum sample size needed.
Chapter 6 Solutions
Elementary Statistics: Picturing the World (7th Edition)
Ch. 6.1 - In Example 1, the researcher selects a second...Ch. 6.1 - Use the data in Try It Yourself 1 and a 95%...Ch. 6.1 - Use the data in Try It Yourself 1 to construct a...Ch. 6.1 - Use the data in Example 1 and technology to...Ch. 6.1 - Construct a 90% confidence interval for the...Ch. 6.1 - In Example 6, how many student-athletes must the...Ch. 6.1 - When estimating a population mean, are you more...Ch. 6.1 - Which statistic is the best unbiased estimator for...Ch. 6.1 - For the same sample statistics, which level of...Ch. 6.1 - You construct a 95% confidence interval for a...
Ch. 6.1 - In Exercises 58, find the critical value Zc...Ch. 6.1 - In Exercises 58, find the critical value Zc...Ch. 6.1 - In Exercises 58, find the critical value Zc...Ch. 6.1 - In Exercises 58, find the critical value Zc...Ch. 6.1 - Graphical Analysis In Exercises 912, use the...Ch. 6.1 - Graphical Analysis In Exercises 912, use the...Ch. 6.1 - Graphical Analysis In Exercises 912, use the...Ch. 6.1 - Graphical Analysis In Exercises 912, use the...Ch. 6.1 - In Exercises 1316, find the margin of error for...Ch. 6.1 - In Exercises 1316, find the margin of error for...Ch. 6.1 - In Exercises 1316, find the margin of error for...Ch. 6.1 - In Exercises 1316, find the margin of error for...Ch. 6.1 - Matching In Exercises 1720, match the level of...Ch. 6.1 - Matching In Exercises 1720, match the level of...Ch. 6.1 - Matching In Exercises 1720, match the level of...Ch. 6.1 - Matching In Exercises 1720, match the level of...Ch. 6.1 - In Exercises 2124, construct the indicated...Ch. 6.1 - In Exercises 2124, construct the indicated...Ch. 6.1 - In Exercises 2124, construct the indicated...Ch. 6.1 - In Exercises 2124, construct the indicated...Ch. 6.1 - In Exercises 2528, use the confidence interval to...Ch. 6.1 - In Exercises 2528, use the confidence interval to...Ch. 6.1 - In Exercises 2528, use the confidence interval to...Ch. 6.1 - In Exercises 2528, use the confidence interval to...Ch. 6.1 - In Exercises 2932, determine the minimum sample...Ch. 6.1 - In Exercises 2932, determine the minimum sample...Ch. 6.1 - In Exercises 2932, determine the minimum sample...Ch. 6.1 - In Exercises 2932, determine the minimum sample...Ch. 6.1 - Finding the Margin of Error In Exercises 33 and...Ch. 6.1 - Finding the Margin of Error In Exercises 33 and...Ch. 6.1 - Constructing Confidence Intervals In Exercises...Ch. 6.1 - Constructing Confidence Intervals In Exercises...Ch. 6.1 - Constructing Confidence Intervals In Exercises...Ch. 6.1 - Constructing Confidence Intervals In Exercises...Ch. 6.1 - In Exercise 35, does it seem possible that the...Ch. 6.1 - In Exercise 36, does it seem possible that the...Ch. 6.1 - In Exercise 37, does it seem possible that the...Ch. 6.1 - In Exercise 38, does it seem possible that the...Ch. 6.1 - When all other quantities remain the same, how...Ch. 6.1 - Constructing Confidence Intervals In Exercises 45...Ch. 6.1 - Constructing Confidence Intervals In Exercises 45...Ch. 6.1 - Determining a Minimum Sample Size Determine the...Ch. 6.1 - Determining a Minimum Sample Size Determine the...Ch. 6.1 - Cholesterol Contents of Cheese A cheese processing...Ch. 6.1 - Ages of College Students An admissions director...Ch. 6.1 - Paint Can Volumes A paint manufacturer uses a...Ch. 6.1 - Juice Dispensing Machine A beverage company uses a...Ch. 6.1 - Soccer Balls A soccer ball manufacturer wants to...Ch. 6.1 - Tennis Balls A tennis ball manufacturer wants to...Ch. 6.1 - When estimating the population mean, why not...Ch. 6.1 - When all other quantities remain the same, how...Ch. 6.1 - Determine the finite population coection factor...Ch. 6.1 - Use the finite population correction factor to...Ch. 6.1 - Sample Size The equation for determining the...Ch. 6.2 - Find the critical value tc for a 90% confidence...Ch. 6.2 - Construct 90% and 99% confidence intervals for the...Ch. 6.2 - Construct 90% and 95% confidence intervals for the...Ch. 6.2 - You randomly select 18 adult male athletes and...Ch. 6.2 - Finding Critical Values of t In Exercises 14, find...Ch. 6.2 - Finding Critical Values of t In Exercises 14, find...Ch. 6.2 - Finding Critical Values of t In Exercises 14, find...Ch. 6.2 - Finding Critical Values of t In Exercises 14, find...Ch. 6.2 - In Exercises 58, find the margin of error for the...Ch. 6.2 - In Exercises 58, find the margin of error for the...Ch. 6.2 - In Exercises 58, find the margin of error for the...Ch. 6.2 - In Exercises 58, find the margin of error for the...Ch. 6.2 - In Exercises 912, construct the indicated...Ch. 6.2 - In Exercises 912, construct the indicated...Ch. 6.2 - In Exercises 912, construct the indicated...Ch. 6.2 - In Exercises 912, construct the indicated...Ch. 6.2 - In Exercises 1316, use the confidence interval to...Ch. 6.2 - In Exercises 1316, use the confidence interval to...Ch. 6.2 - In Exercises 1316, use the confidence interval to...Ch. 6.2 - In Exercises 1316, use the confidence interval to...Ch. 6.2 - Constructing a Confidence Interval In Exercises...Ch. 6.2 - Constructing a Confidence Interval In Exercises...Ch. 6.2 - Constructing a Confidence Interval In Exercises...Ch. 6.2 - Constructing a Confidence Interval In Exercises...Ch. 6.2 - You research commute times to work and find that...Ch. 6.2 - You research driving distances to work and find...Ch. 6.2 - You research prices of cell phones and find that...Ch. 6.2 - You research repair costs of mobile devices and...Ch. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - In Exercise 25, the population mean SAT score is...Ch. 6.2 - In Exercise 28, the population mean weekly time...Ch. 6.2 - Constructing a Confidence Interval Ir. Exercises...Ch. 6.2 - Constructing a Confidence Interval Ir. Exercises...Ch. 6.2 - In Exercise 31, the population mean salary is...Ch. 6.2 - In Exercise 32, the population mean salary is...Ch. 6.2 - Choosing a Distribution In Exercises 3538, use the...Ch. 6.2 - Choosing a Distribution In Exercises 3538, use the...Ch. 6.2 - Choosing a Distribution In Exercises 3538, use the...Ch. 6.2 - Choosing a Distribution In Exercises 3538, use the...Ch. 6.2 - In Exercise 36, does it seem possible that the...Ch. 6.2 - In Exercise 38, does it seem possible that the...Ch. 6.2 - Tennis Ball Manufacturing A company manufactures...Ch. 6.2 - Light Bulb Manufacturing A company manufactures...Ch. 6.2 - Prob. 1ACh. 6.2 - In a random sample of 24 high school students, the...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.3 - A poll surveyed 4780 U.S. adults about how often...Ch. 6.3 - Use the data in Try It Yourself 1 to construct a...Ch. 6.3 - Use the data in Example 3 to construct a 99%...Ch. 6.3 - A researcher is estimating the population...Ch. 6.3 - True or False? In Exercises 1 and 2, determine...Ch. 6.3 - True or False? In Exercises 1 and 2, determine...Ch. 6.3 - Finding p and q In Exercises 36, let p be the...Ch. 6.3 - Finding p and q In Exercises 36, let p be the...Ch. 6.3 - Finding p and q In Exercises 36, let p be the...Ch. 6.3 - Finding p and q In Exercises 36, let p be the...Ch. 6.3 - In Exercises 710, use the confidence interval to...Ch. 6.3 - In Exercises 710, use the confidence interval to...Ch. 6.3 - In Exercises 710, use the confidence interval to...Ch. 6.3 - In Exercises 710, use the confidence interval to...Ch. 6.3 - Constructing Confidence Intervals In Exercises 11...Ch. 6.3 - Constructing Confidence Intervals In Exercises 11...Ch. 6.3 - Constructing Confidence Intervals In Exercises 13...Ch. 6.3 - Constructing Confidence Intervals In Exercises 13...Ch. 6.3 - LGBT Identification In a survey of 1,626,773 U.S....Ch. 6.3 - Transgender Bathroom Policy In a survey of 1000...Ch. 6.3 - Congress You wish to estimate, with 95%...Ch. 6.3 - Genetically Modified Organisms You wish to...Ch. 6.3 - Fast Food You wish to estimate, with 90%...Ch. 6.3 - Alcohol-Impaired Driving You wish to estimate,...Ch. 6.3 - In Exercise 11, does it seem possible that the...Ch. 6.3 - In Exercise 14, does it seem possible that the...Ch. 6.3 - In Exercise 17(b), would a sample size of 200 be...Ch. 6.3 - In Exercise 20(b), would a sample size of 600 be...Ch. 6.3 - Constructing Confidence Intervals In Exercises 25...Ch. 6.3 - Constructing Confidence Intervals In Exercises 25...Ch. 6.3 - Constructing Confidence Intervals In Exercises 27...Ch. 6.3 - Constructing Confidence Intervals In Exercises 27...Ch. 6.3 - Translating Statements In Exercises 2934,...Ch. 6.3 - Translating Statements In Exercises 2934,...Ch. 6.3 - Prob. 31ECh. 6.3 - Translating Statements In Exercises 2934,...Ch. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 1ACh. 6.3 - Prob. 2ACh. 6.4 - Kind the critical values R2 and I2 for a 90%...Ch. 6.4 - Construct the 90% and 95% confidence intervals for...Ch. 6.4 - Does a population have to be normally distributed...Ch. 6.4 - What happens to the shape of the chi-square...Ch. 6.4 - Prob. 3ECh. 6.4 - Finding Critical Values for X2 In Exercises 38,...Ch. 6.4 - Prob. 5ECh. 6.4 - Finding Critical Values for X2 In Exercises 38,...Ch. 6.4 - Finding Critical Values for X2 In Exercises 38,...Ch. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - In Exercises 912, construct the indicated...Ch. 6.4 - Prob. 13ECh. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6 - The waking times (in minutes past 5:00 A.M.) of 40...Ch. 6 - The driving distances (in miles) to work of 30...Ch. 6 - Prob. 6.1.3RECh. 6 - Prob. 6.1.4RECh. 6 - In Exercises 5 and 6, use the confidence interval...Ch. 6 - Prob. 6.1.6RECh. 6 - Prob. 6.1.7RECh. 6 - Prob. 6.1.8RECh. 6 - In Exercises 912, find the critical value tc for...Ch. 6 - In Exercises 912, find the critical value tc for...Ch. 6 - In Exercises 912, find the critical value tc for...Ch. 6 - Prob. 6.2.12RECh. 6 - Prob. 6.2.13RECh. 6 - Prob. 6.2.14RECh. 6 - Prob. 6.2.15RECh. 6 - Prob. 6.2.16RECh. 6 - Prob. 6.2.17RECh. 6 - Prob. 6.2.18RECh. 6 - In Exercises 19-22, let p be the population...Ch. 6 - Prob. 6.3.20RECh. 6 - In Exercises 19-22, let p be the population...Ch. 6 - Prob. 6.3.22RECh. 6 - In Exercise 19, does it seem possible that the...Ch. 6 - Prob. 6.3.24RECh. 6 - Prob. 6.3.25RECh. 6 - Prob. 6.3.26RECh. 6 - Prob. 6.4.27RECh. 6 - Prob. 6.4.28RECh. 6 - Prob. 6.4.29RECh. 6 - In Exercises 2730, find the critical values R2 and...Ch. 6 - Prob. 6.4.31RECh. 6 - In Exercises 31 and 32, assume the sample is from...Ch. 6 - The winning times (in hours) for a sample of 30...Ch. 6 - The data set represents the amounts of time (in...Ch. 6 - Prob. 4CQCh. 6 - Prob. 5CQCh. 6 - Prob. 6CQCh. 6 - Refer to the data set in Exercise 3. Assume the...Ch. 6 - In a survey of 20% U.S. adults, 1740 think...Ch. 6 - The data set represents the weights (in pounds) of...Ch. 6 - The data set represents the scores of 12 randomly...Ch. 6 - Use the standard normal distribution or the...Ch. 6 - The Safe Drinking Water Act, which was passed in...Ch. 6 - The Safe Drinking Water Act, which was passed in...Ch. 6 - The Safe Drinking Water Act, which was passed in...Ch. 6 - Since 1935, the Gallup Organization has conducted...Ch. 6 - THE GALLUP ORGANIZATION www.gallup.com Since 1935,...Ch. 6 - Since 1935, the Gallup Organization has conducted...Ch. 6 - Since 1935, the Gallup Organization has conducted...
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