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elementary statistics
Questions and Answers of
Elementary Statistics
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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?
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
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
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
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
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,
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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).
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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%.
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
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.
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
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