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Elementary Statistics 10th Edition Mario F. Triola - Solutions
6. Estimating Length of Car Ownership A NAPAAuto Parts supplier wants information about how long car owners plan to keep their cars. A simple random sample of 25 car owners results in years and s 5 3.74 years, respectively (based on data from a Roper poll). Assume that the sample is drawn from a
5. Sample Size You have been hired by a consortium of dairy farmers to conduct a survey about the consumption of milk.a. If you want to estimate the percentage of adults who drink milk daily, how many adults must you survey if you want 95% confidence that your sample percentage is in error by no
4. Confidence Interval for s Use the same sample data from Exercise 3 to construct a 95% confidence interval estimate of New specifications are being considered to control the variation of the amounts of coffee that are dispensed. We want almost all of the dispensed amounts to be within 0.5 oz of
3. Vending Machine Specifications for vending machines made by the Newton Machine Company require that they dispense amounts of coffee having a mean of 12 oz.Listed below are amounts of coffee (in ounces) randomly selected from different machines.Use these sample results to construct a 95%
2. Determining Sample Size for a Survey See the survey described in Exercise 1. If you plan to conduct a new poll to confirm that the percentage continues to be correct, how many randomly selected adults must you survey if you want 95% confidence that the margin of error is four percentage points?
1. Alcohol Service Policy In a Gallup poll of 1004 adults, 93% indicated that restaurants and bars should refuse service to patrons who have had too much to drink. Construct a 95% confidence interval estimate of the percentage of all adults who believe that restaurants and bars should refuse
4. Interpreting Confidence Interval Use the confidence interval found in Exercise 3.The media often fail to report the confidence level, but assuming that the confidence interval was found using a 95% confidence level, write a statement that correctly interprets the confidence interval.
3. Margin of Error A newspaper reports survey results by stating that “65% of those surveyed favored the proposition, with a margin of error of 63 percentage points.”What confidence interval is suggested by that statement?
2. Confidence Interval When trying to estimate the mean weight of garbage discarded by households in one week, we obtain these sample results: n 562, lb, s 5 12.46 lb. Knowing that the sample mean is an unbiased estimator of the population mean, we correctly conclude that our best estimate of is
1. Critical Values When working with a normal distribution, the critical value of z 5 1.96 is obtained for a 95% confidence level. What is the relationship between z 5 1.96 and the confidence level of 95%?
28. Finding the Best Estimator We noted that values of s2 tend to produce smaller errors by being closer to than do other unbiased measures of variation. Let’s now consider the biased estimator of Given the population of values {2, 3, 7}, use the value of and use the nine different possible
17. Use the approximation shown here to find the critical values and compare the results to those found from STATDISK.
27. Finding Critical Values In constructing confidence intervals for or we use Table A-4 to find the critical values and but that table applies only to cases in which so the number of degrees of freedom is 100 or smaller. For larger numbers of degrees of freedom, we can approximate and by using
26. Appendix B Data for Weights of Quarters Refer to Data Set 14 in Appendix B and use the sample data.a. Construct a 99% confidence interval estimate of the standard deviation of weights of quarters made after 1964.s.s.mg>m3.mg>m3 Review 375b. Construct a 99% confidence interval estimate of the
25. Appendix B Data for Body Mass Index (BMI) Refer to Data Set 1 in Appendix B and use the sample data.a. Construct a 99% confidence interval estimate of the standard deviation of BMIs for men.b. Construct a 99% confidence interval estimate of the standard deviation of BMIs for women.c. Compare
24.a. Comparing Waiting Lines The listed values are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows. Construct a 95% confidence interval for the population standard deviation 6.5 6.6 6.7 6.8 7.1 7.3
23. Monitoring Lead in Air Listed below are measured amounts of lead (in micrograms per cubic meter, or ) in the air. The Environmental Protection Agency has established an air quality standard for lead of 1.5 The measurements shown below were recorded at Building 5 of the World Trade Center site
22. World’s Smallest Mammal The world’s smallest mammal is the bumblebee bat, also known as the Kitti’s hog-nosed bat (or Craseonycteris thonglongyai). Such bats are roughly the size of a large bumblebee. Listed below are weights (in grams) from a sample of these bats. Construct a 95%
21. Credit Rating When consumers apply for credit, their credit is rated using FICO(Fair, Isaac, and Company) scores. Credit ratings are given below for a sample of applicants for car loans. Use the sample data to construct a 99% confidence interval for the standard deviation of FICO scores for all
20. Shoveling Heart Rates Because cardiac deaths appear to increase after heavy snowfalls, an experiment was designed to compare cardiac demands of snow shoveling to those of using an electric snow thrower. Ten subjects cleared tracts of snow using both methods, and their maximum heart rates (beats
19. Body Temperature Data Set 2 in Appendix B includes 106 body temperatures for which F and F. Using the sample statistics, construct a 99% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Based on the result, can we safely conclude that the
18. Minting Quarters Quarters are currently minted with weights having a mean of 5.670 g and a standard deviation of 0.062 g. New equipment is being tested in an attempt to improve quality by reducing variation. A simple random sample of 24 quarters is obtained from those manufactured with the new
17. Birth Weights In a study of the effects of prenatal cocaine use on infants, the following sample data were obtained for weights at birth: n 5190, g, s 5 645 g(based on data from “Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure,” by Singer et al., Journal of the
16. Find the minimum sample size needed to be 95% confident that the sample variance is within 30% of the population variance.Finding Confidence Intervals. In Exercises 17–24, assume that each sample is a simple random sample obtained from a population with a normal distribution.
15. Find the minimum sample size needed to be 99% confident that the sample variance is within 10% of the population variance. Is such a sample size practical in most cases?
14. Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 20% of
13. Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 5% of
12. Amounts lost by gamblers who took a bus to an Atlantic City casino: 99% confidence;n 5 40, s 5 $87.Determining Sample Size. In Exercises 13–16, assume that each sample is a simple random sample obtained from a normally distributed population.
11. FICO (Fair, Isaac, and Company) credit rating scores of applicants for credit cards:99% confidence; n 5 70, s 5 68.
10. Speeds of drivers ticketed in a 55 mi h zone: 95% confidence; n 5 90, mi h, s 5 3.4 mi h.
9. Salaries of college graduates who took a statistics course in college: 95% confidence;n 5 41, s 5 $18,277.
4. Unbiased Estimators What is an unbiased estimator? Is the sample variance an unbiased estimator of the population variance? Is the sample standard deviation an unbiased estimator of the population standard deviation?Finding Critical Values. In Exercise 5–8, find the critical values and that
3. Interpreting Confidence Intervals For each of the 50 states, a researcher obtains a random sample of credit card debt and calculates the mean to obtain 50 representative values. She then uses the 50 sample means to construct a confidence interval estimate of . Is the result an estimate of the
2. Expressing Confidence Intervals The confidence interval given in Exercise 1 can also be expressed as (2.25, 3.52), but it cannot be expressed as 2.885 6 0.635. Given that 2.885 6 0.635 results in values of 2.25 and 3.52, why can’t we express the confidence interval as 2.885 6 0.635?
1. Interpreting Confidence Interval Using the heights of females listed in Data Set 1 from Appendix B, we use the standard deviation of the sample (s 5 2.741 in.) to obtain the following 95% confidence interval estimate of the standard deviation of the heights of all females: 2.25 in. , ,3.52 in.
33. Confidence Interval for Sample of Size n 5 1 When a manned NASA spacecraft lands on Mars, the astronauts encounter a single adult Martian, who is found to be 12.0 ft tall. It is reasonable to assume that the heights of all Martians are normally distributed.a. The methods of this chapter require
32. Using the Wrong Distribution Assume that a small simple random sample is selected from a normally distributed population for which is unknown. Construction of a confidence interval should use the t distribution, but how are the confidence interval limits affected if the normal distribution is
31. Finite Population Correction Factor If a simple random sample of size n is selected without replacement from a finite population of size N, and the sample size is more than 5% of the population size (n . 0.05N), better results can be obtained by using the finite population correction factor,
30. Alternative Method Figure 7-6 and Table 7-1 summarize the decisions made when choosing between the normal and t distributions. An alternative method included in some textbooks (but almost never included in professional journals) is based on this criterion: Substitute the sample standard
29. Effect of an Outlier Test the effect of an outlier as follows: Use the sample data from Exercise 22 to find a 95% confidence interval estimate of the population mean, after changing the last age from 54 years to 540 years. This value is not realistic, but such an error can easily occur during a
28. Comparing Regular and Diet Pepsi Refer to Data Set 12 in Appendix B and use the sample data.a. Construct a 95% confidence interval estimate of the mean weight of cola in cans of regular Pepsi.b. Construct a 95% confidence interval estimate of the mean weight of cola in cans of Diet Pepsi.c.
27. Pulse Rates A physician wants to develop criteria for determining whether a patient’s pulse rate is atypical, and she wants to determine whether there are significant differences between males and females. Use the sample pulse rates in Data Set 1 from Appendix B.a. Construct a 95% confidence
26. Skull Breadths Maximum breadths of samples of male Egyptian skulls from 4000 B.C. and 150 A.D. (based on data from Ancient Races of the Thebaid by Thomson and Randall-Maciver):4000 B.C.: 131 119 138 125 129 126 131 132 126 128 128 131 150 A.D.: 136 130 126 126 139 141 137 138 133 131 134 129
25. Estimating Car Pollution In a sample of seven cars, each car was tested for nitrogenoxide emissions (in grams per mile) and the following results were obtained: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15 (based on data from the Environmental Protection Agency). Assuming that this sample is
24. World’s Smallest Mammal The world’s smallest mammal is the bumblebee bat, also known as the Kitti’s hog-nosed bat (or Craseonycteris thonglongyai). Such bats are roughly the size of a large bumblebee. Listed below are weights (in grams) from a 362 Chapter 7 Estimates and Sample Sizes
23. Credit Rating When consumers apply for credit, their credit is rated using FICO(Fair, Isaac, and Company) scores. Credit ratings are given below for a sample of applicants for car loans. Use the sample data to construct a 99% confidence interval for the mean FICO score of all applicants for
22. Constructing a Confidence Interval The stemplot below lists the ages of applicants who were successful in winning promotion (based on data from “Debating the Use of Statistical Evidence in Allegations of Age Discrimination,” by Barry and Boland, American Statistician, Vol. 58, No. 2).
21. Monitoring Lead in Air Listed below are measured amounts of lead (in micrograms per cubic meter, or ) in the air. The Environmental Protection Agency has established an air quality standard for lead of 1.5 The measurements shown below were recorded at Building 5 of the World Trade Center site
20. Shoveling Heart Rates Because cardiac deaths appear to increase after heavy snowfalls, an experiment was designed to compare cardiac demands of snow shoveling to those of using an electric snow thrower. Ten subjects cleared tracts of snow using both methods, and their maximum heart rates (beats
19. Forecast and Actual Temperatures Data Set 8 in Appendix B includes a list of actual high temperatures and the corresponding list of three-day-forecast high temperatures.If the difference for each day is found by subtracting the three-day-forecast high temperature from the actual high
18. Mean Body Temperature Data Set 2 in Appendix B includes 106 body temperatures for which F and F. Using the sample statistics, construct a 99%confidence interval estimate of the mean body temperature of all healthy humans. Do the confidence interval limits contain F? What does the sample suggest
17. Birth Weights A random sample of the birth weights of 186 babies has a mean of 3103 g and a standard deviation of 696 g (based on data from “Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure,” by Singer et al., Journal of the American Medical Association, Vol. 291, No.
38. Sample Size Using Sample Data You want to estimate the mean pulse rate of adult males. Refer to Data Set 1 in Appendix B and find the maximum and minimum pulse rates for males, then use those values with the range rule of thumb to estimate How many adult males must you randomly select and test
37. Sample Size Using Range Rule of Thumb You have just been hired by the marketing division of General Motors to estimate the mean amount of money now being spent on the purchase of new cars in the United States. First use the range rule of thumb to s 5 15 s 5 15, 2.58, 7-4 Estimating a Population
36. Sample Size for Television Viewing Nielsen Media Research wants to estimate the mean amount of time (in minutes) that full-time college students spend watching television each weekday. Find the sample size necessary to estimate that mean with a 15-min margin of error. Assume that a 96%
35. Sample Size for Atkins Diet You want to estimate the mean weight loss of people one year after using the Atkins diet. How many dieters must be surveyed if we want to be 95% confident that the sample mean weight loss is within 0.25 lb of the true population mean? Assume that the population
34. Sample Size for Weights of Quarters The Tyco Video Game Corporation finds that it is losing income because of slugs used in its video games. The machines must be adjusted to accept coins only if they fall within set limits. In order to set those limits, the mean weight of quarters in
33. Sample Size for Mean IQ of Statistics Students The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults.Find the sample size necessary to estimate the mean IQ score of statistics students. We want to be 95% confident that our
32. Forecast Errors from Appendix B Refer to Data Set 8 in Appendix B and subtract each actual high temperature from the high temperature that was forecast one day before. The result is a list of errors. Assuming that all such errors have a standard deviation of construct a 95% confidence interval
31. Weights of Quarters from Appendix B Use the weights of post-1964 quarters listed in Data Set 14 from Appendix B. Assuming that quarters are minted to produce weights with a population standard deviation of 0.068 g, use the sample of weights to construct a 99% confidence interval estimate of the
30. World’s Smallest Mammal The world’s smallest mammal is the bumblebee bat, also known as the Kitti’s hog-nosed bat (or Craseonycteris thonglongyai). Such bats are roughly the size of a large bumblebee. Listed below are weights (in grams) from a sample of these bats. Assuming that the
29. Blood Pressure Levels When 14 different second-year medical students at Bellevue Hospital measured the blood pressure of the same person, they obtained the results listed below. Assuming that the population standard deviation is known to be 10 mmHg, construct a 95% confidence interval estimate
28. Cotinine Levels of Smokers When people smoke, the nicotine they absorb is converted to cotinine, which can be measured. A sample of 40 smokers has a mean cotinine level of 172.5. Assuming that is known to be 119.5, find a 90% confidence interval estimate of the mean cotinine level of all
27. Perception of Time Randomly selected statistics students of the author participated in an experiment to test their ability to determine when 1 min (or 60 seconds) has passed. Forty students yielded a sample mean of 58.3 sec. Assuming that sec, construct a 95%confidence interval estimate of the
26. Ages of Motorcyclists Killed in Crashes A study of the ages of motorcyclists killed in crashes involves the random selection of 150 drivers with a mean of 37.1 years (based on data from the Insurance Institute for Highway Safety). Assuming that years, construct a 99% confidence interval
25. Length of Time to Earn Bachelor’s Degree In a study of the length of time that students require to earn bachelor’s degrees, 80 students are randomly selected and they are found to have a mean of 4.8 years (based on data from the National Center for Education Statistics). Assuming that
24. Write a statement that interprets the 95% confidence interval.
23. Express the confidence interval in the format of
22. Express the confidence interval in the format of
21. Identify the value of the point estimate of the population mean
54. Poll Accuracy A New York Times article about poll results states, “In theory, in 19 cases out of 20, the results from such a poll should differ by no more than one percentage point in either direction from what would have been obtained by interviewing all voters in the United States.” Find
53. Rule of Three Suppose n trials of a binomial experiment result in no successes.According to the Rule of Three, we have 95% confidence that the true population proportion has an upper bound of (See “A Look at the Rule of Three,” by Jovanovic and Levy, American Statistician, Vol. 51, No.
52. Interpreting Confidence Interval Limits Assume that a coin is modified so that it favors heads, and 100 tosses result in 95 heads. Find the 99% confidence interval estimate of the proportion of heads that will occur with this coin. What is unusual about the results obtained by the methods of
51. Confidence Interval from Small Sample Special tables are available for finding confidence intervals for proportions involving small numbers of cases, where the normal distribution approximation cannot be used. For example, given x 5 3 successes among n 5 8 trials, the 95% confidence interval
50. One-Sided Confidence Interval A one-sided confidence interval for p can be expressed as or where the margin of error E is modified by replacing with If Air America wants to report an on-time performance of at least x percent with 95% confidence, construct the appropriate one-sided confidence
49. Using Finite Population Correction Factor This section presented Formulas 7-2 and 7-3, which are used for determining sample size. In both cases we assumed that the population is infinite or very large and that we are sampling with replacement. When we have a relatively small population with
48. Accuracy of Forecast Temperatures Refer to Data Set 8 in Appendix B. Construct a 95% confidence interval estimate of the proportion of days with an actual high temperature that is more than 2° different from the high temperature that was forecast one 7-2 Estimating a Population Proportion 337
47. Precipitation in Boston Refer to Data Set 10 in Appendix B, and consider days with precipitation values different from 0 to be days with precipitation. Construct a 95%confidence interval estimate of the proportion of Wednesdays with precipitation, and also construct a 95% confidence interval
46. Alcohol and Tobacco Use in Children’s Movies Refer to Data Set 5 in Appendix B.a. Construct a 95% confidence interval estimate of the percentage of animated children’s movies showing any tobacco use.b. Construct a 95% confidence interval estimate of the percentage of animated children’s
45. Blue M&M Candies Refer to Data Set 13 in Appendix B and find the sample proportion of M&Ms that are blue. Use that result to construct a 95% confidence interval estimate of the population percentage of M&Ms that are blue. Is the result consistent with the 24% rate that is reported by the candy
44. Sunroof and Side Air Bags Toyota provides an option of a sunroof and side air bag package for its Corolla model. This package costs $1400 ($1159 invoice price). Assume that prior to offering this option package, Toyota wants to determine the percentage of Corolla buyers who would pay $1400
43. Nitrogen in Tires A recent campaign was designed to convince car owners that they should fill their tires with nitrogen instead of air. At a cost of about $5 per tire, nitrogen supposedly has the advantage of leaking at a much slower rate than air, so that the ideal tire pressure can be
42. Sample Size for Downloaded Songs The music industry must adjust to the growing practice of consumers downloading songs instead of buying CDs. It therefore becomes important to estimate the proportion of songs that are currently downloaded.How many randomly selected song purchases must be
41. Sample Size for Internet Purchases Many states are carefully considering steps that would help them collect sales taxes on items purchased through the Internet. How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the Internet? Assume
40. Internet Shopping In a Gallup poll, 1025 randomly selected adults were surveyed and 29% of them said that they used the Internet for shopping at least a few times a year.a. Find the point estimate of the percentage of adults who use the Internet for shopping.b. Find a 99% confidence interval
39. Telephone Households In 1920 only 35% of U.S. households had telephones, but that rate is now much higher. A recent survey of 4276 randomly selected households showed that 94% of them had telephones (based on data from the U.S. Census Bureau). Using those survey results, construct a 99%
38. Detecting Fraud When working for the Brooklyn District Attorney, investigator Robert Burton analyzed the leading digits of amounts on checks from companies that were suspected of fraud. Among 784 checks, 61% had amounts with leading digits of 5. Construct a 99% confidence interval estimate of
37. 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 Mexican-Americans. Use the sample data to construct a 99% confidence interval estimate of the
36. Cloning Survey A recent Gallup poll consisted of 1012 randomly selected adults who were asked whether “cloning of humans should or should not be allowed.”Results showed that 901 of those surveyed indicated that cloning should not be allowed. A news reporter wants to determine whether these
35. Cell Phones and Cancer A study of 420,095 Danish cell phone users found that 135 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0340% for those not using cell phones. The data are from the Journal of the
34. Misleading Survey Responses In a survey of 1002 people, 701 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. Find a 99% confidence interval estimate of the proportion of people
33. Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas.a. Find a 95% confidence interval estimate of the percentage of yellow peas.b. Based on his theory of genetics, Mendel expected that 25% of
32. Medical Malpractice An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of them were later dropped or dismissed (based on data from
31. Postponing Death An interesting and popular hypothesis is that individuals can temporarily postpone their death to survive a major holiday or important event such as a birthday. In a study of this phenomenon, it was found that in the week before and the week after Thanksgiving, there were
30. Gender Selection The Genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As this book was being written, 51 babies were born to parents using the YSORT method, and 39 of them were boys. Use the sample data to
4. Sampling A student surveys 100 classmates by asking each if they have outstanding loans. After finding the sample proportion for this sample of n 5 100 subjects, can the methods of this section be used to estimate the proportion of all adults who have outstanding loans? Why or why not?
3. Confidence Interval When surveying 500 people, we get 200 yes responses to a particular question, so the proportion of yes responses from the whole population is estimated to be 0.4. Given that we have the estimated value of 0.4, why would we need a confidence interval? That is, what additional
2. Margin of Error What is a margin of error?
1. Critical Value What is a critical value for a normal distribution?
Problem we noted that touch therapists participated in 280 trials of their ability to sense a human energy field. In each trial, a touch therapist was asked to identify which hand was just below the hand of Emily Rosa. Among the 280 trials, there were 123 correct identifications. The sample results
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