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statistics informed decisions using data

Questions and Answers of Statistics Informed Decisions Using Data

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
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
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.
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
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
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
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
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
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
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
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
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,
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,
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
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
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
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.
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
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
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,
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
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
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
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
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
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,
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
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
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
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
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
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
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:●
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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.
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
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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
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
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
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.
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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