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essential statistics
Essential Statistics 1st Edition David S Moore - Solutions
16.38 Gold in the Yukon. Mining of gold, silver, and lllii copper continues to be big business in Canada's Yukon Territoty. Mining companies release assay results to attract in vestors. Here are the results of gold assays (grams of gold per ton of ore) from 30 test holes at the Sherwood Copper
16.37 How much oil? How much oil wells in a given field will ultimately produce is key information in deciding whether to drill more wells. Here are the estimated total amounts of oil recovered from 64 wells in the Devonian Richmond Dolomite area of the Michigan basin, in thousands of barrels:22
16.36 Weeds among the corn. Velvetleaf is a particularly annoying weed in com fields. It produces lots of seeds, and the seeds wait in the soil for years until conditions are right. How many seeds do velvetleaf plants produce? Here are counts from 28 plants that came up in a corn field when no
16.35 Fungus in the air. Fungus in the air in poultryprocessing plants can affect the health of the workers. The problem is most serious during the summer. To measure the presence of spores, air samples are pumped to an agar plate and"colony-forming units (CPUs)" are counted after an incuba tion
16.34 Growing trees faster. The concentration of carbon dioxide (CO2) iia the atmosphere is increasing due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more GOr may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO2
16.33 Genetic engineering for cancer treatment, contin ued. Another outcome in the cancer experiment described in Exercise 16.32 is measured by a test for the presence of cells that trigger an immune response in the body and so may help fight cancer. Here are data for the 11 subjects: counts of
16.32 Genetic engineering for cancer treatment. Here's a laew idea for treating advanced melanoma, the most serious kind of skin cancer. Genetically engineer white blood cells to better recognize and destroy cancer cells, then infuse these cells into patients. The subjects in a small initial study
16.31 An outlier's effect. A good way to judge the effect of an outlier is to do your analysis twice, once with the outlier and a second time without it. The data in Exercise 16.29 follow a Normal distribution quite closely except for one patient with HAV angle 50 degrees, a high outlier.(a) Find
16.30 An outlier's effect. Our bodies have a natural elec trical field that helps wounds heal. Does changing the field strength slow healing? A series of experiments with newts in vestigated this question. In one experiment, the two hind limbs of 12 newts were assigned at random to either
16.29 A big toe problem. Hallux abducto valgus (call Ki it HAV) is a deformation of the big toe that often requires surgery. Doctors used X-rays to measure the angle (in degrees)of deformity in 3 8 consecutive patients under the age of 21 who came to a medical center for surgery to correct HAV. The
16.28 Learning Blissymbols. Blissymbols ate pictogtapbs(think of Egyptian bietoglypbs) sometimes used to help learning-disabled children. In a study of computer-assisted learning, 12 normal-ability schoolchildren were assigned at random to each of four computer learning programs. After they used
16.27 The conductivity of glass. How well materials conduct beat matters when designing bouses, for example.Conductivity is measured in terms of watts of beat power trans mitted pet scjuate meter of surface pet degree Celsius of temper ature difference on the two sides of the material. In these
16.26 The placebo effect. The placebo effect is particularly strong in patients with Parkinson's disease. To understand the workings of the placebo effect, measure activity at a key point in the brain when patients receive a placebo that they think is an active drug and also when no treatment is
16.25 Calcium and blood pressure. In a randomized com parative experiment on the effect of calcium in the diet on blood pressure, researchers divided 54 healthy white males at random into two groups. One group received calcium;the other, a placebo. At the beginning of the study, the re searchers
16.24 Reading scores in Atlanta. The Trial Urban District Assessment (TUDA) is a government-sponsored study of stu dent achievement in large urban school districts. TUDA gives a reading test scored from 0 to 500. A score of 243 is a "ba sic" reading level and a score of 281 is "proficient." Scores
16.23 Body mass index of young women. In Example 13.1(page 232) we developed a 95% confidence interval for the mean body mass index (BMl) of women aged 20 to 29 yeats, based on a national random sample of 654 such women. We as sumed there that the population standatd deviation was known to be cr =
16.22 Read carefully. You read in the report of a psychol ogy experiment: "Separate analyses for our two groups of 12 participants revealed no overall placebo effect for our student group (mean = 0.08, SD = 0.37, t(ll) = 0.49) and a signif icant effect for our non-student group (mean = 0.35, SD
16.21 Which of these settings does not allow use of a matched pairs t procedure?(a) You interview both the husband and the wife in 64 married couples and ask each about their ideal number of children.(b) You interview a sample of 64 unmarried male students and another sample of 64 unmarried female
16.20 Which of the following would cause the most worry about the validity of the confidence interval you calculated in the previous exercise?(a) There is a clear outlier in the data.(b) A stemplot of the data shows a mild right skew.(c) You do not know the population standard deviation cr.
16.19 Data on the blood cholesterol levels of 24 rats (mil ligrams per deciliter of blood) give x = 85 and s = 12. A 95%confidence interval for the mean blood cholesterol of rats tiiader this condition is(a) 79.9 to 90.1. (b) 80.2 to 89.8. (c) 84.0 to 86.0.
16.18 You have an SRS of 15 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean /x of the popu lation?(a) 2.326 (b) 2.602 (c) 2.624
16.17 You are testing Hq: /u = 10 against Ha", /x < 10 based on an SRS of 20 observations from a Normal population. The t statistic is £ = —2.25. The degrees of freedom for this statistic are(a) 19. (b) 20. (c) 21.
16.16 You are testing Hq: /t = 10 against /t < 10 based on an SRS of 20 observations from a Normal population. The data give x = 8 and s = 4. The value of the t statistic is(a) -0.5. (b) -10. (c) -2.24.
16.15 We prefer the t procedures to the z procedures for infer ence about a population mean because(a) z can be used only for large samples.(b) z requires that you know the population standard devia tion a.(c) z requires that you can regard your data as an SRS from the population.
16.14 Diamonds, continued. Examine the data in Table 16.3 on abundance of carbon-13.Can we use a t confidence interval for mean carhon-13? Explain your answer. Give a 95% confidence interval if you think the result can be trusted.
16.13 Diamonds. Earth scientists studied the small diamonds found in a nodule of rock car ried up to the earth's surface in surrounding rock. This is a sample from a single pop ulation of diamonds formed in a single event deep in the earth.'" Table 16.3 presents data on the nitrogen coirtent (parts
16.12 The brain responds, continued. How much more strongly do monkey brains respond to monkey calls than to pure tones? Give a 90% confidence interval to answer this question.
16.11 The brain responds to sound. The usual way to study the brain's response to sounds is to have subjects listen to "pure tones." The response to recognizable sounds may differ. To compare responses, researchers anesthetized macaque monkeys. They fed pure tones and also monkey calls directly to
16.9 Is it significant? The one-sample t statistic from a sample of n = 25 observations for the two-sided test of Ho: /X = 64 Ff,: /U 64 has the value t = 1.12.(a) What are the degrees of freedom for t ?(b) Locate the two critical values t* from Table C that bracket t. What are the twosided
16.8 Is it significant? The one-sample t statistic for testing Ho: 11 = 0 Ha". II > 0 from a sample of n = 15 observations has the value t = 1.82.(a) What are the degrees of freedom for this statistic?(b) Give the two critical values t* from Table C that bracket t. What are the one-sided P-values
16.7 Ancient air. To discover the nature of the earth's atmosphere long ago, we can examine the gas in bubbles inside ancient amber. Amber is tree resin that has hardened and been trapped in rocks. The gas in bubbles within amber should be a sample of the atmosphere at the time the amber was
16.6 To gamble or not to gamble. Our decisions depend on how the options are presented to us. Here's an experiment that illustrates this phenomenon. Tell 20 subjects that they have been given $50 but can't keep it all. Then present them with a long series of choices between bets they cari make with
16.5 Critical values. What critical value t* from Table C would you use for a confidence interval for the mean of the population in each of the following situations?(a) A 95% confidence interval based on n = 10 observations.(b) A 99% confidence interval from an SRS of 20 observations.(c) A 90%
16.4 More critical values. You have an SRS of size 25 and calculate the one-sample t statis tic. What is the critical value t* such that(a) t has probability 0.025 to the right of t*?(b) t has probability 0.75 to the left of t*?
16.3 Critical values. Use Table C or software to find(a) the critical value for a one-sided test with level a = 0.05 based on the t(5) distri bution.(b) the critical value for a 98% confidence interval based on the t(21) distribution.
16.2 Is that light moving? When two lights close together blink alternately, we "see" one light moving back and forth if the time between blinks is short. What is the longest interval of time between blinks that preserves the illusion of motion? Ask subjects to turn a knob that slows the blinking
16.1 Travel time to work. A study of commuting times reports the travel times to work of a random sample of 20 employed adults in New York State. The mean is x = 31.25 minutes and the standard deviation is s =21.88 minutes. What is the standard error of the mean?
15.59 Do the rich stay that way? We like to think that any one can rise to the top. That's possible, but it's easier if you start near the top. Divide families by the income of the parents into the top 20%, the bottom 20%, and the middle 60%. Here are the conditional probabilities that a child of
15.58 Smoking and social class, continued. Use your work from the previous exercise to find the percent of male smokers who have routine and manual occupations. (Start by expressing this as a conditional probability.) This iniformation is used in planning antismoking campaigns.
15.57 Smoking and social class. As the dangers of smok ing have become more widely known, clear class differences in smoking have emerged. British government statistics clas sify adult men by occupation as "managerial and professional"(43% of the population), "intermediate" (34%), or "routine and
15.56 Cystic fibrosis, continued. Jason tests positive on the CF20m test. What is the probability that he is a carrier of the abnormal CF gene?
15.55 Cystic fibrosis. Cystic fibrosis is a lung disorder that often results in death. It is inherited but can be inherited only if both parents are carriers of an abnormal gene. In 1989, the CF gene that is abnormal in carriers of cystic fibrosis was identified.The probability that a randomly
15.54 Airline overbooking. Airlines sell more tickets than a plane has seats because some passengers don't show up and an empty seat is worth nothing once the plane takes off. You are planning ticket sales for a Boeing 737 with 132 seats. You know that about 12% of people who book the flight won't
15.53 Athletes breaking bones. The intense training needed to reach the Olympics carries risks. About 70% of the members of U.S. Winter Olympics teams have suffered one or more broken bones in the past.(a) The 2006 team had 211 members. What distribution de scribes the number of team members who
15.52 Text messaging. Suppose (as is roughly true) that 40%of all cell phone owners have sent or received text messages. A sample survey interviews an SRS of 2000 cell phone owners.(a) What is the actual distribution of the number X in the sample who have sent or received text messages?(b) What is
15.51 A baseball cliche. How often have you heard a base ball radio or TV announcer say something like "Scott has hit safely in 9 of the last 12 games," as if this were an impressive per formance? Let's find out how impressive. Major league starting players (leaving out pitchers) hit safely in
15.50 Latinos online. "Latinos comprise 14% of the U.S.adult population and about half of this growing group (56%)goes online. Take A to be the event that a raiadomly cho sen adult is a Latino and B the event that a randomly chosen adult goes online. Express the two percents given as probabil
15.49 Comparing wine tasters. In the setting of Exercise 15.38, Taster Ts rating for a wine is 3. What is the conditional probability that Taster 2's rating is higher than 3?
15.48 Really high incomes. The Internal Revenue Service received 138,394,754 individual income tax returns for 2006.Of these, 354,093 reported an adjusted gross income of $1 mil lion or more and 40,931 reported at least $5 million."(a) What is the probability that a randomly chosen return shows an
15.47 Sharing music online. A sample survey reports that 29% of Internet users download music files online, 21% share music files from their computers, and 12% both download and share music.^® Make a Venn diagram that displays this infor mation. What percent of Internet users neither download nor
15.46 Is business success just chance? Investors like to think that some companies are consistently successful. Aca demic researchers looked at data for many companies to de termine whether each firm's sales growth was above the me dian for all firms in each year. They fouiad that a simple "just
15.43 to estimate mean body temperature with 90%confidence. Follow the four-step process for confidence inter vals (page 236).
15.44 Time in a restaurant. Use the data in Exercise k* 15.42 to estimate the mean time customers spend in this restaurant on Saturday evenings with 95% confidence. Follow the four-step process for confidence intervals (page 236).l4 15.45 Normal body temperature. Use the data in Exercise
15.43 Normal body temperature? Here are the daily Bin average body temperatures (degrees Fahrenheit) for 20 healthy adults:'^98.74 97.42 98.54 98.83 97.30 98.33 96.80 97.84 97.87 98.12 100.27 97.48 97.89 97.90 98.92 98.09 99.64 98.33 97.87 97.88(a) Make a stemplot of the data. The distribution is
15.42 Time in a restaurant. The owner of a pizza restau-■it rant in France knows that the time customers spend in the restaurant on Saturday evening has mean 90 minutes and stan dard deviation 15 minutes. He has read that pleasant odors can influence customers, so he spreads a lavender odor
15.38 Comparing wine tasters. Two wine tasters rate each wine they taste on a scale of 1 to 5. From data on their ratings of a large number of wines, we obtain the following probabili ties for both tasters' ratings of a randomly chosen wine (see the chart).with how much a person drinks. The
15.37 The addition rule. The addition rule for probabili ties, P(Aor B) = P(A) 4- P(B), is not always true. Give (in words) an example of real-world events A and B for which this rule is not true.
15.36 Making french fries. Few people want to eat discol ored french fries. Potatoes are kept refrigerated before being cut for french fries to prevent spoiling and preserve flavor. But im mediate processing of cold potatoes causes discoloring due to complex chemical reactions. The potatoes must
15.35 Market research. Stores advertise price reductioias to attract customers. What type of price cut is most attractive?Market researchers prepared ads for athletic shoes announcing different levels of discounts (20%, 40%, or 60%). The student subjects who read the ads were also given "inside
15.34 Fixing health care. The cost of health care and health insurance is the biggest health concern among Americans, even ahead of cancer and other diseases. Chaiaging to a na tional government health insurance system is controversial.An opinion poll will give differeiat results depending on the
15.33 Informed consent. The requirement that human sub jects give their informed consent to participate in an experi ment can greatly reduce the number of available subjects. For example, a study of new teaching methods asks the consent of parents for their children to be taught by either a new
15.32 The placebo effect. A survey of physicians found that some doctors give a placebo to a patient who complains of pain for which the physician can find no cause. If the patient's pain improves, these doctors coiaclude that it had no physical ba sis. The medical school researchers who conducted
15.31 Sampling students. You want to investigate the atti tudes of students at your school toward the school's policy on sexual harassment. You have a grant that will pay the costs of contacting about 500 students.(a) Specify the exact population for your study. For example, will you include
15.34 Fixing health care. The cost of health care and health insurance is the biggest health concern among Americans, even ahead of cancer and other diseases. Chaiaging to a na tional government health insurance system is controversial.An opinion poll will give differeiat results depending on the
15.33 Informed consent. The requirement that human sub jects give their informed consent to participate in an experi ment can greatly reduce the number of available subjects. For example, a study of new teaching methods asks the consent of parents for their children to be taught by either a new
15.32 The placebo effect. A survey of physicians found that some doctors give a placebo to a patient who complains of pain for which the physician can find no cause. If the patient's pain improves, these doctors coiaclude that it had no physical ba sis. The medical school researchers who conducted
15.31 Sampling students. You want to investigate the atti tudes of students at your school toward the school's policy on sexual harassment. You have a grant that will pay the costs of contacting about 500 students.(a) Specify the exact population for your study. For example, will you include
15.30 Brains at work. When our brains store information, complicated chemical changes take place. In trying to under stand these changes, researchers blocked some processes in brain cells taken from rats and compared these cells with a con trol group of normal cells. They say that "no differences
15.29 Does chocolate cause headaches, continued.Here are some of the results of the experiment described in Ex ercise 15.6. There was no significant difference in headaches between the chocolate and carob groups (P = 0.68). But sub jects who said they had a mild headache before eating the candy bar
15.28 An IQ test. The Wechsler Adult Intelligence Scale(WAIS) is a common "IQ test" for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 100 and standard deviation 15.(a) What is the probability that a randomly chosen individual has a WAIS
15.27 Reaction times. The time that people require to react to a stimulus usually has a right-skewed distribution, because lack of attention causes a few lengthy reaction times. Reaction times for children with attention deficit hyperactivity disor der (ADHD) are more skewed, because their
15.26 How many children? How many children do women give birth to dtiring their childbearing years? Choose at random an American woman who is past childbearing:'®Number of children n 0 1 2 3 4 5 Probability 10.193 0.174 0.344 0.181 0.074 _0.034(The few women with 6 or more children are included in
15.25 How many in the house? In government data, a household consists of all occupants of a dwelling unit. Here is the distribution of household size in the United States:Number of persons Probability 1 2 0.26 0.33 30.16 40.15 50.07 60.02 70.01 Choose an American household at random and let the
15.24 Internet search engines. Internet search sites com pete for users because they sell advertising space on their sites and can charge more if they are heavily used. Choose an Internet search attempt at random. Here is the probability dis tribution for the site the search uses:®Site Probability
15.23 Sample space. A randomly chosen subject arrives for a study of exercise and fitness. Describe a sample space for each of the following. (In some cases, you may have some freedom in your choice of S.)(a) The subject is either female or male.(b) After 10 minutes on an exercise bicycle, you ask
15.22 Birth weight and IQ: causation? Very-low-hirthweight babies are more likely to be born to unmarried mothers and to mothers who did not complete high school.(a) Explain why the study of Exetcise 15.20 was not an exper iment.(b) Explain clearly why confounding prevents us from con cluding that
15.21 Birth weight and IQ: testing. IQ tests are scaled so that the mean score in a large population should be /t, =100. We suspect that the very-low-birth-weight population has mean score less than 100. Does the study described in the pre vious exercise give good evidence that this is true? State
15.20 Birth weight and IQ: estimation. Infants weighing less than 1500 grams at bitth are classed as "very low birth weight." Low birth weight carries many risks. One study fol lowed 113 male infants with very low birth weight to adult hood. At age 20, the mean IQ score for these men was x =87.6.^
15.19 Other confidence levels. Use the information in Ex ercise 15.17 to give an 80% confidence iiaterval and a 90% con fidence interval for the mean concentration of dieldrin in the whale population. What general fact about confidence inter vals do the margins of error of your three intervals
15.18 Pesticides in whale blubber: testing. The Food and Drug Administration regulates the amount of dieldrin in raw food. For some foods, no more than 100 ng/g is allowed. Using the information in Exercise 15.17, is there good evidence that the mean concentration in whale blubber is above 100
15.17 Pesticides in whale blubber: estimation. The level of pesticides found in the blubber of whales is a measure of pol lution of the oceans by runoff from land and can also be used to identify different populations of whales. A sample of 8 male minke whales in the West Greetiland area of the
15.16 More significant results. You increase the sample of cross-country runners in Exercise 15.13 from 14 to 56. Sup pose that this larger sample gives the same mean level, x = 4.4 mmol/1. Redo the test in Exercise 15.14. What is the P-value now? At which of the levels a = 0.10, a = 0.05, a = 0.01
15.15 Smaller margin of error. How large a sample is needed to cut the margin of error in Exercise 15.13 in half? How large a sample is needed to cut the margin of error to ±0.1 mmol/1?
15.14 Testing blood cholesterol. The mean blood choles terol level for all Canadian men aged 18 to 34 years is /t, = 4.6 mmol/1. Does the sample in the previous exercise give good ev idence that the meaia for cross-country rurmers is lower? State hypotheses, find the test statistic, and give the
15.13 Blood cholesterol in Canadian men. The distribu tion of blood cholesterol level in the populatioia of Caiaadian men aged 18 to 34 years is close to Normal with staiadard devi ation a = 0.9 millimoles per liter (mmol/1).^ You measure the blood cholesterol of 14 cross-country runners. The mean
15.12 Did you work hard in high school? The average amount of time that high school students spend on homework is about 5 hours per week. Only 25% of college freshmen say they spent at least 6 hours per week on homework in high school. Your college wonders if the average for its freshmen differs
15.11 Fuel economy. The Environmental Protection Agency (EPA) fuel economy ratings say that the Toyota Prius hybrid car gets 48 miles per gallon (mpg) on the highway. Deb orah wonders whether the actual long-term average highway mileage of her new Prius is less than 48 mpg. She keeps care ful
15.10 Marijuana and driving. Questioning a sample of young people in New Zealand revealed a positive associa tion between use of marijuana (cannabis) and traffic accidents caused by the members of the sample. Both cannabis use and accidents were measured by interviewing the young people themselves.
15.9 NOVA takes a sample. The Web site of the PBS tele vision program NOVA Science Now invites viewers to vote on issues such as re-creating the virus responsible for the deadly flu epidemic of 1918. This online poll is unusual in offering de tailed arguments for both sides. Of the 790 viewers who
15.8 Effects of day care. The Carolina Abecedarian Project investigated the effect of high-quality preschool programs on children from poor families. Children were randomly as signed to two groups. One group participated in a year-round preschool program from the age of three months. The control
15.7 Cash to find work? Will cash bonuses speed the re turn to -wotV of unemployed people? The Illinois Department of Employment Security designed an experiment to find out.The subjects were 10,065 people aged 20 to 54 who were filing claims for unemployment insurance. Some were offered $500 if
15.6 Does chocolate cause headaches? The evidence linking chocolates to chronic headaches is inconsistent. In one study, 64 women with chronic headaches ate a restricted diet for two weeks. They then ate candy bars containing either chocolate or carob, prepared to taste the same, and reported
15.5 Elephants and bees. Elephants sometimes damage crops in Africa. It turns out that elephants dislike bees. They recognize beehives in areas where they are common and avoid them. Can this be used to keep elephants away from trees? A group in Kenya placed active beehives in some trees and empty
15.4 California's endangered animals. The California De partment of Fish and Game publishes a list of the state's endan gered animals. Here are the reptiles on the list:Desert tortoise Loggerhead sea turtle Leatherback sea turtle Island night lizard Coachella Valley fringe-toed lizard Southern
15.3 How much do students earn? A university's financial aid office wants to know how much it can expect students to earn from summer employment. This information will be used to set the level of financial aid. The population contains 3478 students who have completed at least one year of study hut
15.2 Student counseling. A university offers its students up to 8 sessions per semester of free psychological counseling. To evaluate satisfaction with this service, the counseling office mails questiormaires to 200 of the 1400 students who partic ipated in counseling last semester. Only 93
15.1 Spoofing. Online criminals use "spoofing" to direct In ternet users to fraudulent Web sites in order to collect informa tion such as passwords. In one study of Internet fraud, students were warned about spoofing and then asked to log in to their university account starting from the
14.33 A test goes wrong. Software can generate samples from (almost) exactly Normal distributions. Here is a random sample of size 5 from the Normal distribution with mean 10 and standard deviation 2:6.47 7.51 10.10 13.63 9.91 These data match the conditions for a ?: test better than real data
14.32 Predicting success of trainees. What distinguishes managerial trainees who eventually become executives from those who don't succeed and leave the company? We have lots of data on past trainees—data on their personalities and goals, their college preparation and performance, even their
14.31 Why are larger samples better? Statisticians prefer large samples. Describe briefly the effect of increasing the size of a sample (or the number of subjects in an experiment) on each of the following:(a) The margin of error of a 95% confidence interval.(b) The P -value of a test, when Ho is
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