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elementary statistics
Elementary Statistics 9th Edition Mario F. Triola - Solutions
Weights of Bears The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9 lb. Assuming that s is known to be 121.8 lb, find a 99% confidence interval estimate of the mean of
Everglades Temperatures In order to monitor the ecological health of the Florida Everglades, various measurements are recorded at different times. The bottom temperatures are recorded at the Garfield Bight station and the mean of 30.4°C is obtained for 61 temperatures recorded on 61 different
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 the
Women’s Heights Women’s heights are normally distributed with a mean of 63.6 in.and a standard deviation of 2.5 in. How many women must be surveyed if we want to estimate the percentage who are taller than 5 ft? Assume that we want 98% confidence that the error is no more than 2.5 percentage
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 3 n. (See “A Look at the Rule of Three,” by Jovanovic and Levy, American Statistician, Vol. 51, No.
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 this
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 found
One-Sided Confidence Interval A one-sided confidence interval for p can be expressed as p , 1 E or p . 2 E, where the margin of error E is modified by replacing with za. If Air America wants to report an on-time performance of at least x percent with 95% confidence, construct the appropriate
Using Finite Population Correction Factor This section presented Formulas 6-2 and 6-3, 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 size N
Probing for Precision An example of this section used the photo-cop survey data with n 5 829 and 5 0.51 to construct the 95% confidence interval of 0.476 , p , 0.544.However, cannot be exactly 0.51 because 51% of 829 people is 422.79 people, which is not possible. The sample statistic of 51% has
Alcohol and Tobacco Use in Children’s Movies Refer to Data Set 7 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
Red M&M Candies Refer to Data Set 19 in Appendix B and find the sample proportion of M&Ms that are red. Use that result to construct a 95% confidence interval estimate of the population percentage of M&Ms that are red. Is the result consistent with the 20% rate that is reported by the candy maker
Appearance Counts A Sales and Marketing Management survey included 651 sales managers, and 94% of them said that being a sloppy dresser can make a sales representative’s job more difficult. For that same group, 75% said that being an unstylish dresser can make a sales representative’s job more
Wearing Hunter Orange A study of hunting injuries and the wearing of “hunter”orange clothing showed that among 123 hunters injured when mistaken for game, 6 were wearing orange. Among 1115 randomly selected hunters, 811 reported that they routinely wear orange. The data are from the Centers for
Pilot Fatalities Researchers studied crashes of general aviation (noncommercial and nonmilitary) airplanes and found that pilots died in 5.2% of 8411 crash landings(based on data from “Risk Factors for Pilot Fatalities in General Aviation Airplane Crash Landings,” by Rostykus, Cummings, and
Cell Phones and Cancer A study of 420,000 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
TV Ratings The CBS television show 60 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 60 Minutes (based on data from Nielsen Media Research). Assume that this is based on a sample size of 4000 (typical for
Color Blindness In a study of perception, 80 men are tested and 7 are found to have red green color blindness (based on data from USA Today).a. Construct a 90% confidence interval estimate of the proportion of all men with this type of color blindness.b. What sample size would be needed to estimate
Sample Size for Weapons on Campus Concerned about campus safety, college officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. How many randomly selected students must be surveyed in order to be 95%confident that the sample percentage has a margin of
Sample Size for Motor Vehicle Ownership You have been hired by the Ford Motor Company to do market research, and you must estimate the percentage of households in which a vehicle is owned. How many households must you survey if you want to be 94% confident that your sample percentage has a margin
Sample Size for Left-Handed Golfers As a manufacturer of golf equipment, the Spalding Corporation wants to estimate the proportion of golfers who are left-handed.(The company can use this information in planning for the number of right-handed and left-handed sets of golf clubs to make.) How many
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 that
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
Drug Testing The drug Ziac is used to treat hypertension. In a clinical test, 3.2% of 221 Ziac users experienced dizziness (based on data from Lederle Laboratories).a. Construct a 99% confidence interval estimate of the percentage of all Ziac users who experience dizziness.b. In the same clinical
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 who
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 the
Death Penalty Survey In a Gallup poll, 491 randomly selected adults were asked whether they are in favor of the death penalty for a person convicted of murder, and 65% of them said that they were in favor.a. Find the point estimate of the percentage of adults who are in favor of this death
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
Interpreting Calculator Display 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 4019 of them had telephones (based on data from the U.S.Census Bureau). Using those survey results and a 99%
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 left-handed.c.
Eye Measurement Statistics The listed sample distances (in millimeters) were obtained by using a pupilometer to measure the distances between the pupils of adults(based on data collected by a student of the author).67 66 59 62 63 66 66 55a. Find the mean of the distances in this sample.b. Find the
Testing for Normality Refer to the weights of sugar packets, as listed in Data Set 28 in Appendix B. Do those weights appear to come from a population that has a normal distribution? Explain.Cumulative Review Exercises
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 2 women and 18 men. Find the probability of randomly selecting 20 people
Sampling Distributionsa. Many different samples of size 100 are randomly selected from the weights of cars currently registered in the United States. What can be concluded about the shape of the distribution of the means of the different samples?b. If the weights of all cars registered in the
Uniform Distribution The San Francisco Supply Company has designed a machine that fills containers of coffee in such a way that the contents are uniformly distributed with a minimum of 11.8 oz and a maximum of 12.2 oz. If one container is randomly selected, find the probability that the amount of
Marine Corps Height Requirements for Men The U.S. Marine Corps requires that men have heights between 64 in. and 78 in. (The National Health Survey shows that heights of men are normally distributed with a mean of 69.0 in. and a standard deviation of 2.8 in.)a. Find the percentage of men meeting
Blue Genes Some couples have genetic characteristics configured so that one-quarter of all their offspring have blue eyes. A study is conducted of 100 couples believed to have those characteristics, with the result that 19 of their 100 offspring have blue eyes. Assuming that one-quarter of all
Babies at Risk Weights of newborn babies in the United States are normally distributed with a mean of 3420 g and a standard deviation of 495 g (based on data from“Birth Weight and Prenatal Mortality,” by Wilcox et al., Journal of the American Medical Association, Vol. 273, No. 9).a. A newborn
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 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 probability
Lognormal Distribution The random variable x is said to have a lognormal distribution if the values of ln x are normally distributed. Test the following phone call times(in seconds) for normality, then test for normality of the natural logarithms of the times. What do you conclude?31.5 75.9 31.8
Using Standard Scores When constructing a normal quantile plot, suppose that instead of finding z scores using the procedure described in this section, each value in a sample is converted to its corresponding standard score using z 5 (x 2 ) s. If the(x, z) points are plotted in a graph, can this
Monitoring Lead in Air On the days immediately following the destruction caused by the terrorist attacks on September 11, 2001, lead amounts (in micrograms per cubic meter) in the air were recorded at Building 5 of the World Trade Center site, and these values were obtained: 5.40, 1.10, 0.42, 0.73,
Heights of L.A. Lakers Use this sample of heights (in inches) of the players in the starting lineup for the L.A. Lakers professional basketball team: 85, 79, 82, 73, 78.
Comparing Data Sets Using the systolic blood pressure levels and the elbow breadths of women, as listed in Data Set 1 in Appendix B, analyze each of the two data sets and determine whether each appears to come from a normally distributed population.Compare the results and give a possible
Comparing Data Sets Using the heights of women and the cholesterol levels of women, as listed in Data Set 1 in Appendix B, analyze each of the two data sets and determine whether each appears to come from a normally distributed population.Compare the results and give a possible explanation for any
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?
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 gets
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 years (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
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 a
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
Car Crashes For drivers in the 20–24 age bracket, there is a 34% rate of car accidents in one year (based on data from the National Safety Council). An insurance investigator finds that in a group of 500 randomly selected drivers aged 20–24 living in New York City, 40% had accidents in the last
Acceptance Sampling We stated in Section 3-4 that 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 particular size includes more than some specified number of defects. The Dayton Machine Company buys
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 blood,
M&M Candies: Are 10% Blue? According to a consumer affairs representative from Mars (the candy company, not the planet), 10% of all M&M plain candies are blue.Data Set 19 in Appendix B shows that among 100 M&Ms chosen, 5 are blue. Estimate the probability of randomly selecting 100 M&Ms and getting
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 her
On-Time Flights Recently, American Airlines had 72.3% of its flights arriving on time (based on data from the U.S. Department of Transportation). In a check of 40 randomly selected American Airlines flights, 19 arrived on time. Estimate the probability of getting 19 or fewer on-time flights among
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 persons,
Cell Phones and Brain Cancer In a study of 420,000 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 therefore
Probability of at Least 50 Color-Blind Men Nine percent of men and 0.25% of women cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals. Researchers need at least 50 men with this type of color blindness, so they randomly
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 symptoms
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
Multiple-Choice Test A multiple-choice test consists of 25 questions with possible answers ofa, b,c, d, ande. Estimate the probability that with random guessing, the number of correct answers is between 3 and 10 inclusive.
Probability of at Least Passing Estimate the probability of passing a true false test of 100 questions if 60% (or 60 correct answers) is the minimum passing grade and all responses are random guesses. Is that probability high enough to risk passing by using random guesses instead of studying?
Probability of at Least 65 Girls Estimate the probability of getting at least 65 girls in 100 births. Assume that boys and girls are equally likely. Is it unusual to get at least 65 girls in 100 births?
Probability of More than 55 Girls Estimate the probability of getting more than 55 girls in 100 births. Assume that boys and girls are equally likely. Is it unusual to get more than 55 girls in 100 births?
Uniform Random-Number Generator In Exercise 10 it was noted that many calculators and computers have a random-number generator that yields numbers from a uniform distribution of values between 0 and 1, with a mean of 0.500 and a standard deviation of 0.289. If 100 random numbers are generated, find
Population Parameters A population consists of these values: 2, 3, 6, 8, 11, 18.a. Find m and s.b. List all samples of size n 5 2 that can be obtained without replacement.c. Find the population of all values of by finding the mean of each sample from part (b).d. Find the mean and standard deviation
Correcting for a Finite Population The Boston Women’s club needs an elevator limited to 8 passengers. The club has 120 women members with weights that approximate a normal distribution with a mean of 143 lb and a standard deviation of 29 lb.(Hint: See the discussion of the finite population
Seating Design You need to build a bench that will seat 18 male college football players, and you must first determine the length of the bench. Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.0 in.a. What is the minimum length of the bench
Elevator Design Women’s weights are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men’s weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb (based on data from the National Health Survey). You need to design an elevator
Labeling of M&M Packages M&M plain candies have a mean weight of 0.9147 g and a standard deviation of 0.0369 g (based on Data Set 19 in Appendix B). The M&M candies used in Data Set 19 came from a package containing 1498 candies, and the package label stated that the net weight is 1361 g. (If every
Overloading of Waste Disposal Facility The town of Newport operates a rubbish waste disposal facility that is overloaded if its 4872 households discard waste with weights having a mean that exceeds 27.88 lb in a week. For many different weeks, it is found that the samples of 4872 households have
Coaching for the SAT Test Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112 (based on data from the College Board). Randomly selected men are given the Columbia Review Course before taking the SAT test. Assume that the
Reduced Nicotine in Cigarettes The amounts of nicotine in Dytusoon cigarettes have a mean of 0.941 g and a standard deviation of 0.313 g (based on Data Set 5 in Appendix B). The Huntington Tobacco Company, which produces Dytusoon cigarettes, claims that it has now reduced the amount of nicotine.
Blood Pressure For women aged 18–24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1 (based on data from the National Health Survey). Hypertension is commonly defined as a systolic blood pressure above 140.a. If a woman between
Mean Replacement Times The manager of the Portland Electronics store is concerned that his suppliers have been giving him TV sets with lower than average quaity. His research shows that replacement times for TV sets have a mean of 8.2 years and a standard deviation of 1.1 years (based on data from
IQ Scores Membership in Mensa requires an IQ score above 131.5. Nine candidates take IQ tests, and their summary results indicated that their mean IQ score is 133. (IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.)a. If 1 person is randomly selected, find the
Amounts of Coke Assume that cans of Coke are filled so that the actual amounts have a mean of 12.00 oz and a standard deviation of 0.11 oz.a. Find the probability that a sample of 36 cans will have a mean amount of at least 12.19 oz, as in Data Set 17 in Appendix B.b. Based on the result from part
Uniform Random-Number Generator The random-number generator on the TI-83 Plus calculator and many other calculators and computers yields numbers from a uniform distribution of values between 0 and 1, with a mean of 0.500 and a standard deviation of 0.289. If 100 random numbers are generated, find
Designing a Roller Coaster The Rock ’n’ Roller Coaster at Disney–MGM Studios in Orlando has two seats in each row. When designing that roller coaster, the total width of the two seats in each row had to be determined. In the “worst case” scenario, both seats are occupied by men. Men have
Designing Motorcycle Helmets Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 in. and a standard deviation of 1.0 in. (based on anthropometric survey data from Gordon, Churchill, et al.).a.
Redesign of Ejection Seats In the Chapter Problem, it was noted that engineers were redesigning fighter jet ejection seats to better accommodate women. Before women became fighter jet pilots, the ACES-II ejection seats were designed for men weighing between 140 lb and 211 lb. The population of
Median as an Estimator In Table 5-2, the sampling distribution of the medians has a mean of 2.7. Because the population mean is also 2.7, it might appear that the median is a good statistic for estimating the value of the population mean. Using the population values 1, 2, 5, find the 27 samples of
Mean Absolute Deviation The population of 1, 2, 5 was used to develop Table 5-2.Identify the sampling distribution of the mean absolute deviation (defined in Section 2-5), then determine whether the mean absolute deviation of a sample is a good statistic for estimating the mean absolute deviation
Here is the population of all five U.S. presidents who had professions in the military, along with their age at inauguration: Eisenhower (62), Grant (46), Harrison (68), Taylor (64), and Washington (57). Assume that all samples are selected without replacement.a. After listing all of the possible
Women Senators Let a population consist of these home states of all three female Republican senators in the 107th Congress of the United States: Maine, Maine, Texas.Assuming that samples of size 2 are randomly selected from this population without replacement, list the different possible samples.
Women Senators Let a population consist of the 10 Democrats and 3 Republicans who are women senators in the 107th Congress of the United States.a. Develop a procedure for randomly selecting (with replacement) a sample of size 5 from the population of 10 Democrats and 3 Republicans, then select such
Quality Control After constructing a new manufacturing machine, 5 prototype car headlights are produced and it is found that 2 are defective (D) and 3 are acceptable(A). Assume that two headlights are randomly selected with replacement from this population.a. After identifying the 25 different
Genetics A genetics experiment involves a population of fruit flies consisting of 1 male named Mike and 3 females named Anna, Barbara, and Chris. Assume that two fruit flies are randomly selected with replacement.a. After identifying the 16 different possible samples, find the proportion of females
Military Presidents Here is the population of all five U.S. presidents who had professions in the military, along with their ages at inauguration: Eisenhower (62), Grant(46), Harrison (68), Taylor (64), and Washington (57). Assume that samples of size 2 are randomly selected with replacement from
Heights of L.A. Lakers Here are the heights (in inches) of the five starting basketball players for the L.A. Lakers: 85, 79, 82, 73, 78.Assume that samples of size 2 are randomly selected with replacement from the above population of five heights.a. After identifying the 25 different possible
Telemarketing Here are the numbers of sales per day that were made by Kim Ryan, a courteous telemarketer who worked four days before being fired: 1, 11, 9, 3. Assume that samples of size 2 are randomly selected with replacement from this population of four values.a. List the 16 different possible
Phone Center The Nome Ice Company was in business for only three days (guess why). Here are the numbers of phone calls received on each of those days: 10, 6, 5.Assume that samples of size 2 are randomly selected with replacement from this population of three values.a. List the 9 different possible
Sampling Distribution of Survey Results The Gallup organization conducted a poll of 1015 randomly selected students in grades K through 12 and found that 10% attended private or parochial schools.a. Is the 10% (or 0.10) result a statistic or a parameter? Explain.b. What is the sampling distribution
Sampling Distribution of Body Temperatures Data Set 4 in Appendix B includes a sample of 106 body temperatures of adults. If we were to construct a histogram to depict the shape of the distribution of that sample, would that histogram show the shape of a sampling distribution of sample means? Why
Sampling Distribution of Harry Potter Data Set 14 in Appendix B includes a sample of measured reading levels for 12 pages randomly selected from J. K. Rowling’s Harry Potter and the Sorcerer’s Stone. The mean of the 12 Flesch-Kincaid grade level values is 5.08. The value of 5.08 is one value
Survey of Voters Based on a random sample of n 5 400 voters, the NBC news division predicts that the Democratic candidate for the presidency will get 49% of the vote, but she actually gets 51%. Should we conclude that the survey was done incorrectly? Why or why not?
SAT and ACT Tests Scores by women on the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202. Scores by women on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.6. Assume that the two tests use different scales to measure
SAT Scores According to data from the College Entrance Examination Board, scores on the SAT-I test have a mean of 1017, and Q1 is 880. The scores have a distribution that is approximately normal. Find the standard deviation, then use that result to find P99.
Curving Test Scores A teacher informs her psychology class that a test is very difficult, but the grades will be curved. Scores for the test are normally distributed with a mean of 25 and a standard deviation of 5.a. If she curves by adding 50 to each grade, what is the new mean? What is the new
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