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Elementary Statistics 10th Edition Mario F. Triola - Solutions
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
2. Left-Handedness According to data from the American Medical Association, 10% of us are left-handed.a. If three people are randomly selected, find the probability that they are all lefthanded.b. If three people are randomly selected, find the probability that at least one of them is
1. Carbohydrates in Food Some standard food items are randomly selected and the carbohydrate contents (in grams) are measured with the results listed below (based on data from the U.S. Department of Agriculture). (The items are 12 oz of regular coffee, one cup of whole milk with 3.3% fat, one egg,
6. Testing for Normality Listed below are the lengths of time (in days) that the New York State budget has been late for each of 19 consecutive and recent years. Do those lengths of time appear to come from a population that has a normal distribution? Why or why not?4 4 10 19 18 48 64 1 4 68 67 103
5. Gender Discrimination When several women are not hired at the Telektronics Company, they do some research and find that among the many people who applied, 30% were women. However, the 20 people who were hired consist of only 3 women and 17 men. Find the probability of randomly selecting 20
4. Detecting Gender Bias in a Test Question When analyzing one particular question on an IQ test, it is found that among the 20 people who answered incorrectly, 18 are women. Given that the test was given to the same number of men and women, all carefully chosen so that they have the same
3. High Cholesterol Levels The serum cholesterol levels in men aged 18–24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7. Units are in mg 100 mL, and the data are based on the National Health Survey.a. If one man aged 18–24 is randomly selected, find the
2. Boston Beanstalk Club The Boston Beanstalk Club has a minimum height requirement of 74 in. for men. Heights of men are normally distributed with a mean of 69.0 in.and a standard deviation of 2.8 in. (based on data from the National Health Survey).a. What percentage of men meet the minimum height
1. Weighing Errors A scale is designed so that when items are weighed, the errors in the indicated weights are normally distributed with a mean of 0 g and a standard deviation of 1 g. (If the scale reading is too low, the error is negative. If the scale reading is too high, the error is
4. Central Limit Theorem What does the central limit theorem tell us?
3. Simple Random Sample A researcher has collected a large sample of IQ scores from friends and relatives. He claims that because his sample is large and the distribution of his sample scores is very close to the bell shape of a normal distribution, his sample is representative of the population.
2. Distribution of Sample Means A process consists of randomly selecting 250 adults, measuring the grip strength (right hand only), then finding the sample mean. Assuming that this process is repeated many times, what important fact do we know about the distribution of the resulting sample means?
1. Normal Distribution What is a normal distribution? What is a standard normal distribution?
37. Normal Approximation Required This section included the statement that “In reality, almost all practical applications of the binomial probability distribution can now be handled well with software or a TI-83 84 Plus calculator.” Using a specific software package or a TI-83 84 Plus
36. Overbooking Flights Vertigo Airlines works only with advance reservations and experiences a 7% rate of no-shows. How many reservations could be accepted for an airliner with a capacity of 250 if there is at least a 0.95 probability that all reservation holders who show will be accommodated?
35. Joltin’ Joe Assume that a baseball player hits .350, so his probability of a hit is 0.350.(Ignore the complications caused by walks.) Also assume that his hitting attempts are independent of each other.a. Find the probability of at least 1 hit in 4 tries in 1 game.b. Assuming that this batter
34. Replacement of TVs Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 year (based on data from “Getting Things Fixed,” Consumer Reports). Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have
33. Winning at Roulette Marc Taylor plans to place 200 bets of $1 each on the number 7 at roulette. A win pays off with odds of 35:1 and, on any one spin, there is a probability of 1 38 that 7 will be the winning number. Among the 200 bets, what is the minimum number of wins needed for Marc to make
32. 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, 479 had amounts with leading digits of 5, but checks issued in the normal course of honest
31. Detecting Credit Card Fraud The Dynamic Credit company issues credit cards and uses software to detect fraud. After tracking the spending habits of one consumer, it is found that charges over $100 constitute 35.8% of the credit transactions. Among 30 charges made this month, 18 involve totals
30. Bias in Jury Selection In Orange County, 12% of those eligible for jury duty are lefthanded.Among 250 people selected for jury duty, 25 (or 10%) are lefties. Find the probability of getting at most 25 lefties asssuming that they are chosen with a process designed to yield a 12% rate of lefties.
29. 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 89% of those surveyed indicated that cloning should not be allowed. A news reporter wants to determine whether these
28. Acceptance Sampling Some companies monitor quality by using a method of acceptance sampling, whereby an entire batch of items is rejected if a random sample of a 6-6 Normal as Approximation to Binomial 301 particular size includes more than some specified number of defects. The Dayton Machine
27. Blood Group Forty-five percent of us have Group O blood, according to data provided by the Greater New York Blood Program. Providence Memorial Hospital is conducting a blood drive because its supply of Group O blood is low, and it needs 177 donors of Group O blood. If 400 volunteers donate
26. M&M Candies: Are 20% Orange? According to Mars (the candy company, not the planet), 20% of M&M plain candies are orange. Data Set 13 in Appendix B shows that among 100 M&Ms chosen, 25 are orange. Assuming that the claimed orange M&Ms rate of 20% is correct, estimate the probability of randomly
25. Identifying Gender Discrimination After being rejected for employment, Kim Kelly learns that the Bellevue Advertising Company has hired only 21 women among its last 62 new employees. She also learns that the pool of applicants is very large, with an equal number of qualified men and women. Help
24. Overbooking Flights Air America is considering a new policy of booking as many as 400 persons on an airplane that can seat only 350. (Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.) Estimate the probability that if Air America books 400
23. Cell Phones and Brain Cancer In a study of 420,095 cell phone users in Denmark, it was found that 135 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is a 0.000340 probability of a person developing cancer of the brain or nervous system. We
22. Cholesterol Reducing Drug The probability of flu symptoms for a person not receiving any treatment is 0.019. In a clinical trial of Lipitor, a common drug used to lower cholesterol, 863 patients were given a treatment of 10-mg atorvastatin tablets, and 19 of those patients experienced flu
21. Mendel’s Hybridization Experiment When Mendel conducted his famous hybridization experiments, he used peas with green pods and yellow pods. One experiment involved crossing peas in such a way that 25% (or 145) of the 580 offspring peas were expected to have yellow pods. Instead of getting 145
20. TV Advertising Charges for advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is a percentage of the population of 110 million TV households. The CBS television show 60 Minutes recently had a rating of 7.8, indicating that 7.8% of the
19. Voters Lying? 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. Given that 61% of eligible voters actually did vote, find the probability that among
18. Probability of at Least 42 Girls Assuming that boys and girls are equally likely, estimate the probability of getting at least 42 girls in 64 births. Is it unusual to get at least 42 girls in 64 births?
17. Probability of More Than 36 Girls Assuming that boys and girls are equally likely, estimate the probability of getting more than 36 girls in 64 births. Is it unusual to get more than 36 girls in 64 births?
4. Interpreting Binomial Probability In a test of a method of gender selection, 80 couples are given a treatment designed to increase the likelihood that a baby will be a girl. There were 47 girls among the 80 babies born. If the gender-selection method has no effect, the probability of getting
3. Distribution of Sample Proportions The Newport Bottling plant produces bottles of cola that are packaged in six-packs. The probability of a defective bottle is 0.001. Can we approximate the distribution of defects in six-packs as a normal distribution? Why or why not?
1. Distribution of Sample Proportions Consider a study in which we obtain records from the next 50 babies that are born, then compute the proportion of girls in this sample. Assume that this study is repeated many times, and the sample proportions are used to construct a histogram. What is the
3. SAT Math Scores of Women The math SAT scores for women are normally distributed with a mean of 496 and a standard deviation of 108.a. If a woman who takes the math portion of the SAT is randomly selected, find the probability that her score is above 500.b. If five math SAT scores are randomly
2. Normal Quantile Plot Refer to the data listed in Exercise 1 and construct a normal quantile plot. Based on the result, do the heights appear to come from a population that is normally distributed?
1. Heights of Presidents Listed below are the heights (in inches) of the Presidents who served in the 20th century. Assume that these values are sample data from some larger population.67 70 72 71 72 70 71 74 69 70.5 72 75 71.5 69.5 73 74 74.5a. Find the mean.b. Find the median.c. Find the standard
12. Nicotine in Cigarettes The Carolina Tobacco Company advertised that its best-selling nonfiltered cigarettes contain at most 40 mg of nicotine, but Consumer Advocate magazine ran tests of 10 randomly selected cigarettes and found the amounts (in mg)shown in the accompanying list. It’s a
11. Umpire Strike Rate In a recent year, some professional baseball players complained that umpires were calling more strikes than the average rate of 61.0% called the previous year. At one point in the season, umpire Dan Morrison called strikes in 2231 of 3581 pitches (based on data from USA
10. Heights of Women Anthropometric survey data are used to publish values that can be used in designing products that are suitable for use by adults. According to Gordon, Churchill, et al., women have heights with a mean of 64.1 in. and a standard deviation of 2.52 in. The sample of 40 heights of
9. Body Temperature Apremed student in a statistics class is required to do a class project.Intrigued by the body temperatures in Data Set 2 of Appendix B, she plans to collect her own sample data to test the claim that the mean body temperature is less than 98.6°F, as is commonly believed.
8. Random Generation of Data The TI-83 84 Plus calculator can be used to generate random data from a normally distributed population. The command randNorm(100,15,50)generates 50 values from a normally distributed population with m 5 100 and s 5 15.One such generated sample of 50 values has a mean
7. IQ Scores For a simple random sample of adults, IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Asimple random sample of 13 statistics professors yields a standard deviation of s 5 7.2. A psychologist is quite sure that statistics professors have IQ scores
6. Testing Lipitor for Adverse Effects In clinical tests of the drug Lipitor (generic name, atorvastatin), 863 patients were treated with 10-mg doses of atorvastatin, and 19 of those patients experienced flu symptoms (based on data from Parke-Davis). Use a 0.01 significance level to test the claim
5. Are Consumers Being Cheated? The Orange County Bureau of Weights and Measures received complaints that the Windsor Bottling Company was cheating consumers by putting less than 12 oz of root beer in its cans. When 24 cans are randomly selected and measured, the amounts are found to have a mean of
4. Weights of Sugar Packets A student of the author randomly selected 70 packets of sugar and weighed the contents of each packet, getting a mean of 3.586 g and a standard deviation of 0.074 g. Test the claim that the weights of the sugar packets have a mean equal to 3.5 g, as indicated on the
3. Glamour Magazine Survey Glamour magazine sponsored a survey of 2500 prospective brides and found that 60% of them spent less than $750 on their wedding gown.Use a 0.01 significance level to test the claim that less than 62% of brides spend less than $750 on their wedding gown. How are the
2. Interviewing Mistakes An Accountemps survey of 150 executives showed that 44%of them say that “little or no knowledge of the company” is the most common mistake made by candidates during job interviews (based on data from USA Today). Use a 0.05 significance level to test the claim that less
1. Identifying Hypotheses, Distributions, and Verifying Requirements Based on the given conditions, identify the alternative hypothesis. Also, either identify the sampling distribution(normal, t, chi-square) of the test statistic, or state that the methods of this chapter should not be used.Table
2. Sample You have just collected a very large (n 5 2575) sample of responses obtained from adult Americans who mailed responses to a questionnaire printed in Fortune magazine. If this sample is used to make inferences about a population, what is the population? A hypothesis test conducted at the
1. Practical Significance When testing the claim that the mean amount lost on a diet is greater than 0 lb, we use sample results showing that 10,000 people lost amounts with a mean of 0.1 lb. Also, the sample standard deviation is 0.8 lb. The hypothesis test results include a test statistic of t 5
20. Appendix B Data for Precipitation Amounts Refer to Data Set 8 in Appendix B and use the sample data consisting of the precipitation amounts. Test the claim that these amounts are from a population with a standard deviation less than 1.00 in. Use a significance level of 0.05. Does the
19. Appendix B Data for Weights of Quarters Refer to Data Set 14 in Appendix B and use the sample data consisting of weights of quarters made after 1964. Test the claim that these quarters come from a population with a standard deviation equal to the specified value of 0.068 g. Use a significance
17. 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 The measurements shown below were recorded at Building 5 of the World Trade Center site on
16. Supermodel Heights Use a 0.05 significance level to test the claim that heights of female supermodels vary less than the heights of women in general. The standard deviation of heights of the population of women is 2.5 in. Listed below are the 8-6 Testing a Claim About a Standard Deviation or
14. 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. Using a 0.05
13. 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, and these applicants are all from a new branch of the Bank of Newport. Use the sample data to test the claim
12. Manufacturing Aircraft Altimeters The Stewart Aviation Products Company uses a new production method to manufacture aircraft altimeters. A simple random sample of 81 altimeters is tested in a pressure chamber, and the errors in altitude are recorded as positive values (for readings that are too
11. Variation in Peanut M&Ms Use a 0.01 significance level to test the claim that peanut M&M candies have weights that vary more than the weights of plain M&M candies.The standard deviation for the weights of plain M&M candies is 0.056 g. A sample of 41 peanut M&Ms has weights with a standard
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