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statistics informed decisions using data
Elementary Statistics 10th Edition Mario F. Triola - Solutions
21. Flying In a Gallup poll of 1125 adults, it was found that 47% fly never or rarely. Use a 0.05 significance level to test the claim that the percentage of adults who fly never or rarely is equal to 50%. Given that the survey subjects volunteered an answer to a question about flying, is it
20. Smoking In a Gallup poll of 1018 adults, it was found that 22% smoked cigarettes in the past week. Use a 0.05 significance level to test the claim that less than 25% of adults have smoked within the past week. Would the conclusion change if, instead of a Gallup poll, the results were obtained
19. Drinking Survey A recent Gallup poll of 976 randomly selected adults showed that 312 of them never drink. Use those survey results to test the claim that less than 1 3 of all adults never drink. Use a 0.05 significance level. Also, examine the following wording of the actual question and
18. 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 there were 6062 deaths in the week before Thanksgiving, and there
17. Store Checkout Scanner Accuracy In a study of store checkout scanners, 1234 items were checked and 20 checked items were found to be overcharges, and 1214 checked items were not overcharges (based on data from “UPC Scanner Pricing Systems: Are They Accurate?” by Goodstein, Journal of
16. Testing Effectiveness of Nicotine Patches In one study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment, and 32 were not smoking one year after the treatment (based on data from “High-Dose Nicotine Patch Therapy,” by Dale et al.,
15. Cell Phones and Cancer In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today). Test the claim of a once Minitab Display for Exercise 8 416 Chapter 8
14. Drug Testing of Job Applicants In 1990, 5.8% of job applicants who were tested for drugs failed the test. At the 0.01 significance level, test the claim that the failure rate is now lower if a simple random sample of 1520 current job applicants results in 58 failures (based on data from the
13. Percentage of E-Mail Users Technology is dramatically changing the way we communicate.In 1997, a survey of 880 U.S. households showed that 149 of them use e-mail (based on data from The World Almanac and Book of Facts). Use those sample results to test the claim that more than 15% of U.S.
12. Travel Through the Internet Among 734 randomly selected Internet users, it was found that 360 of them use the Internet for making travel plans (based on data from a Gallup poll). Use a 0.01 significance level to test the claim that among Internet users, less than 50% use it for making travel
11. Car Crashes In a study of 11,000 car crashes, it was found that 5720 of them occurred within 5 miles of home (based on data from Progressive Insurance). Use a 0.01 significance level to test the claim that more than 50% of car crashes occur within 5 miles of home. Are the results questionable
10. Gender Selection for Boys 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
9. Gender Selection for Girls The Genetics and IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl. As this book was being written, 325 babies were born to parents using the XSORT method, and 295 of them were girls. Use the sample
8. Percentage of Telephone Users Asurvey of 4276 randomly selected households showed that 4019 of them had telephones (based on data from the U.S. Census Bureau). Minitab was used to test the claim that the percentage of households is now greater than the 35%rate that was found in 1920. The Minitab
7. Interpreting Display When 109,857 arrests for federal offenses were randomly selected, it was found that 31,969 of them were drug offenses. When testing the claim that more than 29% of federal crimes were for drug offenses, the accompanying TI-83 84 Plus calculator display was obtained. Use the
6. Survey of Workers In a survey of 703 randomly selected workers, 15.93% got their jobs through newspaper ads (based on data from Taylor Nelson Sofres Intereach).Consider a hypothesis test that uses a 0.05 significance level to test the claim that less than 20% of workers get their jobs through
5. Mendel’s Hybridization Experiments In one of Mendel’s famous hybridization experiments, 8023 offspring peas were obtained, and 24.94% of them had green flowers.The others had white flowers. Consider a hypothesis test that uses a 0.05 significance level to test the claim that green-flowered
4. P-Value Method A P-value of 0.00001 is obtained when using sample data to test the claim that the majority of car crashes occur within 5 miles of home. Interpret this P-value in the context of this hypothesis test. That is, what does the P-value tell us?In Exercises 5–8, identify the indicated
3. Sampling America Online conducts a survey in which Internet users are asked to respond to a question. Among the 96,772 responses, there are 76,885 responses of“yes.” Is it valid to use these sample results for testing the claim that the majority of the general population answers “yes”?
2. Sample Proportion When respondents are asked a question on a survey, 40 of them answer yes, 60 of them answer no, and there are no other responses. What is the sample proportion of yes responses, and what notation is used to represent it?
1. Distribution Assuming that the listed requirements of this section are satisfied, what distribution is used to test a claim about a population proportion? Why?
48. Finding Sample Size Aresearcher plans to conduct a hypothesis test using the alternative hypothesis of H1: p , 0.4, and she plans to use a significance level of a 5 0.05.Find the sample size required to achieve at least 80% power in detecting a reduction in p from 0.4 to 0.3. (This is a very
Assume that you are using a significance level of a 5 0.05 to test the claim that p . 0.5 and that your sample is a simple random sample of size n 5 64.a. Assuming that the true population proportion is 0.65, find the power of the test, which is the probability of rejecting the null hypothesis when
11. Out-of-class activity Each student should find an article in a professional journal that includes a confidence interval of the type discussed in this chapter. Write a brief report describing the confidence interval and its role in the context of the article.
10. Out-of-class activity Identify a topic of general interest and coordinate with all members of the class to conduct a survey. Instead of conducting a “scientific” survey using sound principles of random selection, use a convenience sample consisting of respondents that are readily available,
9. In-class activity Divide into groups of two. First find the sample size required to estimate the proportion of times that a coin turns up heads when tossed, assuming that you want 80% confidence that the sample proportion is within 0.08 of the true population proportion.Then toss a coin the
8. In-class activity Divide into groups of three or four. Examine a current magazine such as Time or Newsweek, and find the proportion of pages that include advertising.Based on the results, construct a 95% confidence interval estimate of the percentage of all such pages that have advertising.
7. In-class activity Each student should estimate the length of the classroom. The values should be based on visual estimates, with no actual measurements being taken. After the estimates have been collected, construct a confidence interval, then measure the length of the room. Does the confidence
6. In-class activity A class project should be designed to conduct a test in which each student is given a taste of Coke and a taste of Pepsi. The student is then asked to identify which sample is Coke. After all of the results are collected, analyze the claim that the success rate is better than
5. In-class activity Each student should write an estimate of the age of the current President of the United States.All estimates should be collected and the sample mean and standard deviation should be calculated. Then use the sample results to construct a confidence interval.Do the confidence
4. Out-of-class activity Groups of three or four students should go to the library and collect a sample consisting of the ages of books (based on copyright dates). Plan and describe the sampling plan, execute the sampling procedure, then use the results to construct a confidence interval estimate
3. In-class activity Assume that a method of gender selection can affect the probability of a baby being a girl, so that the probability becomes Each student should simulate 20 births by drawing 20 cards from a shuffled deck. Replace each card after it has been drawn, then reshuffle. Consider the
2. In-class activity Without using any measuring device, each student should draw a line believed to be 3 in.long and another line that is 3 cm long. Then use rulers to measure and record the lengths of the lines drawn. Find the means and standard deviations of the two sets of lengths. Use the
1. Out-of-class activity Collect sample data, and use the methods of this chapter to construct confidence interval estimates of population parameters. Here are some suggestions for parameters:● Proportion of students at your college who can raise one eyebrow without raising the other eyebrow.
3. Estimating Theme Park Attendance Each year, billions of dollars are spent at theme parks owned by Disney, Universal Studios, Sea World, Busch Gardens, and others. A survey includes 111 people who took trips that included visits to theme parks, and there were 1122 other respondents who took trips
2. X-Linked Recessive Disorders A genetics expert has determined that for certain couples, there is a 0.25 probability that any child will have an X-linked recessive disorder.a. Find the probability that among 200 such children, at least 65 have the X-linked recessive disorder.b. A subsequent study
1. Analyzing Weights of Supermodels Supermodels are sometimes criticized on the grounds that their low weights encourage unhealthy eating habits among young women.Listed below are the weights (in pounds) of nine randomly selected supermodels.125 (Taylor) 119 (Auermann) 128 (Schiffer) 128
8. Crash Hospital Costs A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution that appears to be bell-shaped with a mean of $9004 and a standard deviation of $5629(based on data from the U.S. Department of
7. Smoking and College Education The tobacco industry closely monitors all surveys that involve smoking. One survey showed that among 785 randomly selected subjects who completed four years of college, 18.3% smoke (based on data from the American Medical Association).a. Construct the 98% confidence
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
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