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statistics for experimentert
Introduction To Statistics And Data Analysis 5th Edition Roxy Peck, Chris Olsen, Jay L Devore - Solutions
●● that the value of a sample statistic varies from sample to sample.
CR7.21 ● The following data are a sample of survival times (days from diagnosis) for patients suffering from chronic leukemia of a certain type:7 47 58 74 177 232 273 285 317 429 440 445 455 468 495 497 532 571 579 581 650 702 715 779 881 900 930 968 1077 1109 1314 1334 1367 1534 1712 1784 1877
CR7.20 ● The paper “The Load-Life Relationship for M50 Bearings with Silicon Nitride Ceramic Balls” (Lubrication Engineering [1984]: 153–159) reported the accompanying data on bearing load life (in millions of revolutions). The corresponding normal scores are also given.x Normal Score x
CR7.19 Consider the variable x 5 time required for a college student to complete a standardized exam Suppose that for the population of students at a particular university, the distribution of x is well approximated by a normal distribution with mean 45 minutes and standard deviation 5 minutes.a.
CR7.18 A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 inches. A bearing is acceptable if its diameter is within 0.004 inches of this target value.Suppose, however, that the setting has changed during the course of
CR7.17 An experiment was conducted to investigate whether a graphologist (a handwriting analyst) could distinguish a normal person’s handwriting from that of a psychotic.A well-known expert was given 10 files, each containing handwriting samples from a normal person and from a person diagnosed as
CR7.16 Return to the previous exercise, and let y denote the amount of material (in pounds) left after the next customer’s order is shipped. Find the mean and variance of y. (Hint: y is a linear function of x.)
CR7.15 A chemical supply company currently has in stock 100 pounds of a certain chemical, which it sells to customers in 5-pound lots. Let x 5 the number of lots ordered by a randomly chosen customer. The probability distribution of x is as follows:x 1 2 3 4 p(x) .2 .4 .3 .1a. Calculate the mean
CR7.12 The article “Men, Women at Odds on Gun Control”(Cedar Rapids Gazette, September 8, 1999) included the following statement: “The survey found that 56% of American adults favored stricter gun control laws. Sixty-six percent of women favored the tougher laws, compared with 45% of men.”
CR7.11 According to a study conducted by a risk assessment firm (Associated Press, December 8, 2005), drivers residing within 1 mile of a restaurant are 30% more likely to be in an accident in a given policy year. Consider the following two events:A 5 event that a driver has an accident during a
CR7.10 The Cedar Rapids Gazette (November 20, 1999)reported the following information on compliance with child restraint laws for cities in Iowa:City Number of Children Observed Number Properly Restrained Cedar Falls 210 173 Cedar Rapids 231 206 Dubuque 182 135 Iowa City (city) 175 140 Iowa City
3. Doctors misdiagnosed heart attacks in 7% of women under 55 years old.Use the following event definitions:M 5 event that a heart attack is misdiagnosed, B 5 event that a patient is black, and W 5 event that a patient is a woman under 55 years old.Translate each of the three given statements into
2. Doctors misdiagnosed heart attacks in 4.3% of black patients.
1. Doctors misdiagnosed heart attacks in 2.1% of all patients.
CR7.9 The article “Doctors Misdiagnose More Women, Blacks” (San Luis Obispo Tribune, April 20, 2000) gave the following information, which is based on a large study of more than 10,000 patients treated in emergency rooms in the eastern and midwestern United States:
CR7.8 The paper “The Effect of Temperature and Humidity on Size of Segregated Traffic Exhaust Particle Emissions”(Atmospheric Environment [2008]: 2369–2382) gave the following summary quantities for a measure of traffic flow(vehicles/second) during peak traffic hours at a particular location
CR7.6 ● Manatees are large marine mammals found along the coast of Florida. Data on the total number of manatee deaths per year reported by the Florida Marine Research Center is given in the accompanying table. Construct a time series plot of these data and comment on any trends over time.Year
CR7.5 Beverly is building a fireplace. She is using special decorative 8-inch bricks for the bottom row of the fireplace.Although the bricks are advertised as 8-inch bricks, the actual length of a brick is variable, and the brick lengths are approximately normally distributed with a mean of 8
CR7.4 The following quote is from USA Today (January 21, 2010):Most Americans think the Census is important, and the majority say they will participate in the count this spring—although Hispanics, younger people and the less educated are not as enthusiastic, a Pew Research Center survey found.
CR7.3 Red-light cameras are used in many places to deter drivers from running red lights. The following graphical display is similar to one that appeared in the article “Communities Put a Halt to Red-Light Cameras” (USA Today, January 18, 2010). Based on this graph, would it be correct to
CR7.2 ● The article “Water Consumption in the Bay Area”(San Jose Mercury News, January 16, 2010) reported the accompanying values for water consumption (gallons per person per day) for residential customers of 27 San Francisco Bay area water agencies:49 52 53 59 59 61 69 70 70 73 79 80 85 87
7.126 There are approximately 40,000 travel agencies in the United States, of which 11,000 are members of the American Society of Travel Agents (booking a tour through an ASTA member increases the likelihood of a refund in the event of cancellation).a. If x is the number of ASTA members among 5000
7.125 The lightbulbs used to provide exterior lighting for a large office building have an average lifetime of 700 hours. If length of life is approximately normally distributed with a standard deviation of 50 hours, how often should all the bulbs be replaced so that no more than 20% of the bulbs
7.124 Suppose that the pH of soil samples taken from a certain geographic region is normally distributed with a mean pH of 6.00 and a standard deviation of 0.10. If the pH of a randomly selected soil sample from this region is determined, answer the following questions about it:a. What is the
7.123 Suppose that your statistics professor tells you that the scores on a midterm exam were approximately normally distributed with a mean of 78 and a standard deviation of 7. The top 15% of all scores have been designated A’ s. Your score is 89. Did you receive an A? Explain.
7.122 Refer to the previous exercise, and let y be the number of games won by the series loser. Determine the probability distribution of y.
7.121 Kyle and Lygia are going to play a series of Trivial Pursuit games. The first person to win four games will be declared the winner. Suppose that outcomes of successive games are independent and that the probability of Lygia winning any particular game is .6. Define a random variable x as the
7.119 Two sisters, Allison and Teri, have agreed to meet between 1 and 6 p.m. on a particular day. In fact, Allison is equally likely to arrive at exactly 1 p.m., 2 p.m., 3 p.m., 4 p.m., 5 p.m., or 6 p.m. Teri is also equally likely to arrive at each of these six times, and Allison’s and Teri’s
7.118 The longest “run” of S’s in the sequence SSFSSSSFFS has length 4, corresponding to the S’s on the fourth, fifth, sixth, and seventh positions. Consider a binomial experiment with n 5 4, and let y be the length in the longest run of S’s.a. When p 5 .5, the 16 possible outcomes are
7.117 The Wall Street Journal (February 15, 1972) reported that General Electric was sued in Texas for sex discrimination over a minimum height requirement of 5 ft. 7 in. The suit claimed that this restriction eliminated more than 94% of adult females from consideration. Let x represent the height
7.116 A machine producing vitamin E capsules operates so that the actual amount of vitamin E in each capsule is normally distributed with a mean of 5 mg and a standard deviation of 0.05 mg. What is the probability that a randomly selected capsule contains less than 4.9 mg of vitamin E? at least 5.2
7.115 The lifetime of a certain brand of battery is normally distributed with a mean value of 6 hours and a standard deviation of 0.8 hours when it is used in a particular DVD player. Suppose that two new batteries are independently selected and put into the player. The player ceases to function as
7.114 The amount of time spent by a statistical consultant with a client at their first meeting is a random variable having a normal distribution with a mean value of 60 minutes and a standard deviation of 10 minutes.a. What is the probability that more than 45 minutes is spent at the first
7.113 The probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table:x 0 1 2 3 4 p(x) .54 .16 .06 .04 .20 The mean value of x is mx 5 1.2. Calculate the values of s 2x and sx.
7.112 A coin is flipped 25 times. Let x be the number of flips that result in heads (H). Consider the following rule for deciding whether or not the coin is fair:Judge the coin fair if 8 # x # 17.Judge the coin biased if either x # 7 or x $ 18.a. What is the probability of judging the coin biased
7.111 Suppose that fuel efficiency for a particular model car under specified conditions is normally distributed with a mean value of 30.0 mpg and a standard deviation of 1.2 mpg.a. What is the probability that the fuel efficiency for a randomly selected car of this type is between 29 and 31 mpg?b.
7.110 A pizza company advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas.Suppose that the amount of cheese on a randomly selected medium pizza is normally distributed with a mean value of 0.5 pounds and a standard deviation of 0.025 pounds.a. What is the probability
7.109 A new battery’s voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 80% of all batteries have acceptable voltages, and let y denote the
7.107 A business has six customer service telephone lines.Let x denote the number of lines in use at a specified time. Suppose that the probability distribution of x is as follows:x 0 1 2 3 4 5 6 p(x) .10 .15 .20 .25 .20 .06 .04 Write each of the following events in terms of x, and then calculate
7.106 A soft-drink machine dispenses only regular Coke and Diet Coke. Sixty percent of all purchases from this machine are diet drinks. The machine currently has 10 cans of each type. If 15 customers want to purchase drinks before the machine is restocked, what is the probability that each of the
7.105 Let x denote the duration of a randomly selected pregnancy (the time elapsed between conception and birth). Accepted values for the mean value and standard deviation of x are 266 days and 16 days, respectively. Suppose that the probability distribution of x is (approximately) normal.a. What
4. Combine the observations from your group with those from the other groups. Use the resulting data to approximate the distribution of x. Comment on the resulting distribution in the context of the risk of salmonella exposure if the manager’s proposed procedure is used.
3. Suppose that a carton of one dozen eggs does happen to have exactly three eggs that carry salmonella and that the manager does as he proposes: selects three eggs at random and throws them out, then uses the remaining nine eggs in four-egg quiches. Let x 5 number of eggs that carry salmonella
2. Suppose the following argument is made for threeegg quiches rather than four-egg quiches: Let x # number of eggs that carry salmonella. Then p(0) 5 p(x 5 0) 5 (0.75)3 5 .422 for three-egg quiches and p(0) 5 p(x 5 0) 5 (0.75)4 5 .316 for four-egg quiches. What assumption must be made to justify
1. Working in a group or as a class, discuss the folly of the above statement!
2. Working as a group, each student in your class should flip a coin 30 times and note the number of heads in the 30 tosses. If there are fewer than 50 students in the class, each student should repeat this process until there are a total of at least 50 observations of x 5 number of heads in 30
1. Do you think that any of the three students made up the x values shown in their dotplot? If so, which ones, and what about the dotplot makes you think the student did not actually do the coin flipping?
7.104 A company that manufactures mufflers for cars offers a lifetime warranty on its products, provided that ownership of the car does not change. Suppose that only 20% of its mufflers are replaced under this warranty.a. In a random sample of 400 purchases, what is the approximate probability that
7.102 Suppose that 65% of all registered voters in a certain area favor a 7-day waiting period before purchase of a handgun. Among 225 randomly selected registered voters, what is the approximate probability thata. At least 150 favor such a waiting period?b. More than 150 favor such a waiting
7.99 Studies have found that women diagnosed with cancer in one breast also sometimes have cancer in the other breast that was not initially detected by mammogram or physical examination (“MRI Evaluation of the Contralateral Breast in Women with Recently Diagnosed Breast Cancer,” The New
7.98 Symptom validity tests (SVTs) are sometimes used to confirm diagnosis of psychiatric disorders. The paper“Developing a Symptom Validity Test for Post-Traumatic Stress Disorder: Application of the Binomial Distribution”(Journal of Anxiety Disorders [2008]: 1297–1302)investigated the use
7.97 Suppose that x has a binomial distribution with n 5 50 and p 5 .6, so that m 5 np 5 30 and s 5Ïnps12pd 5 3.4641. Approximate the following probabilities using the normal approximation with the continuity correction. (Hint: See Example 7.35.)a. P(x 5 30)b. P(x 5 25)c. P(x # 25)d. P(25 # x #
7.96 The number of vehicles leaving a turnpike at a certain exit during a particular time period has approximately a normal distribution with mean value 500 and standard deviation 75. What is the approximate probability that the number of cars exiting during this period isa. at least 650?b.
7.95 Suppose that the distribution of x 5 the number of items produced by an assembly line during an 8-hour shift can be approximated by a normal distribution with mean value 150 and standard deviation 10.a. What is the approximate probability that the number of items produced is at most 120?b.
7.94 Let x denote the IQ of an individual selected at random from a certain population. The value of x must be a whole number. Suppose that the distribution of x can be approximated by a normal distribution with mean value 100 and standard deviation 15. Approximate the following probabilities.
7.93 The following figure appeared in the paper “EDTAExtractable Copper, Zinc, and Manganese in Soils of the Canterbury Plains” (New Zealand Journal of Agricultural Research [1984]: 207–217). A large number of topsoil samples were analyzed for manganese (Mn), zinc(Zn), and copper (Cu), and
7.92 ● The paper “Temperature and the Northern Distributions of Wintering Birds” (Ecology [1991]:2274–2285) gave the following body masses (in grams) for 50 different bird species:7.7 10.1 21.6 8.6 12.0 11.4 16.6 9.4 11.5 9.0 8.2 20.2 48.5 21.6 26.1 6.2 19.1 21.0 28.1 10.6 31.6 6.7 5.0 68.8
7.91 The article “The Distribution of Buying Frequency Rates” (Journal of Marketing Research [1980]: 210–216)reported the results of a 312-year study of toothpaste purchases. The investigators conducted their research using a national sample of 2071 households and recorded the number of
7.90 ● Example 7.32 examined rainfall data for Minneapolis–St. Paul. The square-root transformation was used to obtain a distribution of values that was more nearly symmetric than the distribution of the original data. Another transformation that has been suggested by meteorologists is the cube
7.89 ● Consider the following sample of 25 observations on the diameter x (in centimeters) of a disk used in a certain system:16.01 16.08 16.13 15.94 16.05 16.27 15.89 15.84 15.95 16.10 15.92 16.04 15.82 16.15 16.06 15.66 15.78 15.99 16.29 16.15 16.19 16.22 16.07 16.13 16.11 The 13 largest normal
7.88 ● Consider the following 10 observations on the lifetime (in hours) for a certain type of power supply: 152.7, 172.0, 172.5, 173.3, 193.0, 204.7, 216.5, 234.9, 262.6, and 422.6. Construct a normal probability plot, and comment on the plausibility of a normal distribution as a model for power
7.87 The following normal probability plot was constructed using part of the data appearing in the paper “Trace Metals in Sea Scallops” (Environmental Concentration and Toxicology 19: 1326–1334).+--+ ----+----++-----+-----+-----+-----+-----+-1.60 -0.80 0.00 0.80 1.60 2.40 Observation Normal
7.86 ● Macular degeneration is the most common cause of blindness in people older than 60 years. One variable thought to be related to a type of inflammation associated with this disease is level of a substance called soluble Fas ligand (sFasL) in the blood.The accompanying table contains
7.85 ● Measures of nerve conductivity are used in the diagnosis of certain medical conditions. The paper“Effects of Age, Gender, Height, and Weight on Late Responses and Nerve Conduction Study Parameters”(Acta Neurologica Taiwanica [2009]: 242–249) describes a study in which the ulnar nerve
7.84 ● The paper “Risk Behavior, Decision Making, and Music Genre in Adolescent Males” (Marshall University, May 2009) examined the effect of type of music playing and performance on a risky, decision-making task.a. Participants in the study responded to a questionnaire that was used to
7.83 ● The authors of the paper “Development of Nutritionally At-Risk Young Children is Predicted by Malaria, Anemia, and Stunting in Pemba, Zanzibar” (The Journal of Nutrition [2009]:763–772) studied factors that might be related to dietary deficiencies in children. Children were observed
7.82 ▼ Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 60 wpm and standard deviation 15 wpm (“The Effects of Split Keyboard Geometry on Upper body
7.79 Refer to the previous exercise. Suppose that there are two machines available for cutting corks. The machine described in the preceding problem produces corks with diameters that are approximately normally distributed with mean 3 cm and standard deviation 0.1 cm. The second machine produces
7.78 A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter for the corks produced is well approximated by a normal distribution with mean 3 cm and standard deviation 0.1 cm. The specifications call for corks with diameters between 2.9 and 3.1 cm. A
7.74 The paper referenced in Example 7.30 (“Estimating Waste Transfer Station Delays Using GPS,” Waste Management [2008]: 1742–1750) describing processing times for garbage trucks also provided information on processing times at a second facility. At this second facility, the mean total
7.73 Emissions of nitrogen oxides, which are major constituents of smog, can be modeled using a normal distribution. Let x denote the amount of this pollutant emitted by a randomly selected vehicle (in parts per billion). The distribution of x can be described by a normal distribution with m 5 1.6
7.72 Consider babies born in the “normal” range of 37–43 weeks gestational age. The paper referenced in Example 7.27 (“Fetal Growth Parameters and Birth Weight: Their Relationship to Neonatal Body Composition,” Ultrasound in Obstetrics and Gynecology[2009]: 441–446) suggests that a
7.71 Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean m 5 5 ml and standard deviation s 5 0.2 ml is a reasonable model for the distribution of the variable x 5 amount of red dye in the paint
7.70 Because P(z , .44) 5 .67, 67% of all z values are less than .44, and .44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution (Hint: If the cumulative area that you must look for does not
7.69 Determine the value of z* such thata. 2z* and z* separate the middle 95% of all z values from the most extreme 5% (Hint: See Example 7.26.)b. 2z* and z* separate the middle 90% of all z values from the most extreme 10%c. 2z* and z* separate the middle 98% of all z values from the most extreme
7.68 Determine the value z* thata. Separates the largest 3% of all z values from the others (Hint: See Example 7.26.)b. Separates the largest 1% of all z values from the othersc. Separates the smallest 4% of all z values from the othersd. Separates the smallest 10% of all z values from the others
b. P(z , z*) 5 .01c. P(z , z*) 5 .05d. P(z . z*) 5 .02e. P(z . z*) 5 .01f. P(z . z* or z , 2z*) 5 .20
7.67 Let z denote a variable that has a standard normal distribution. Determine the value z* to satisfy the following conditions. (Hint: See Example 7.25.)a. P(z , z*) 5 .025
7.66 Let z denote a random variable having a normal distribution with m 5 0 and s 5 1. Determine each of the following probabilities. (Hint: See Examples 7.27 and 7.28.)a. P(z , 0.10)b. P(z , 20.10)c. P(0.40 , z , 0.85)d. P(20.85 , z , 20.40)e. P(20.40 , z , 0.85)f. P(z . 21.25)g. P(z , 21.50 or z
7.62 ▼ The article on polygraph testing of FBI agents referenced in Exercise 7.51 indicated that the probability of a false-positive (a trustworthy person who nonetheless fails the test) is .15. Let x be the number of trustworthy FBI agents tested until someone fails the test.a. Describe the
7.60 Sophie is a dog that loves to play catch. Unfortunately, she isn’t very good, and the probability that she catches a ball is only .1. Let x be the number of tosses required until Sophie catches a ball.a. Does x have a binomial or a geometric distribution?b. What is the probability that it
7.59 Suppose a playlist on an MP3 music player consists of 100 songs, of which eight are by a particular artist.Suppose that songs are played by selecting a song at random (with replacement) from the playlist. The random variable x represents the number of songs played until a song by this artist
7.58 Suppose that 90% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of 25 registered California voters is to be selected.a. What is the probability that more than 20
7.57 A city ordinance requires that a smoke detector be installed in all residential housing. There is concern that too many residences are still without detectors, so a costly inspection program is being contemplated.Let p be the proportion of all residences that have a detector. A random sample
7.56 Suppose that 20% of the 10,000 signatures on a certain recall petition are invalid. Would the number of invalid signatures in a sample of 2000 of these signatures have(approximately) a binomial distribution? Explain.
7.55 You are to take a multiple-choice exam consisting of 100 questions with five possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question.Let x represent the number of correct responses
7.54 Thirty percent of all automobiles undergoing an emissions inspection at a certain inspection station fail the inspection.a. Among 15 randomly selected cars, what is the probability that at most five fail the inspection?b. Among 15 randomly selected cars, what is the probability that between
7.53 Suppose that the probability is .1 that any given citrus tree will show measurable damage when the temperature falls to 308F. (Hint: See Example 7.21.)a. If the temperature does drop to 308F, what is the expected number of citrus trees showing damage in orchards of 2000 trees?b. What is the
7.52 Industrial quality control programs often include inspection of incoming materials from suppliers.If parts are purchased in large lots, a typical plan might be to select 20 parts at random from a lot and inspect them. A lot might be judged acceptable if one or fewer defective parts are found
7.51 The article “FBI Says Fewer than 25 Failed Polygraph Test” (San Luis Obispo Tribune, July 29, 2001) states that false-positives in polygraph tests (tests in which an individual fails even though he or she is telling the truth) are relatively common and occur about 15%of the time. Suppose
7.48 Example 7.18 described a study in which a person was asked to determine which of three t-shirts had been worn by her roommate by smelling the shirts (“Sociochemosensory and Emotional Functions,”Psychological Science [2009]: 1118–1123). Suppose that instead of three shirts, each
7.47 Twenty-five percent of the customers of a grocery store use an express checkout. Consider five randomly selected customers, and let x denote the number among the five who use the express checkout.a. What is p(2), that is, P(x 5 2)?b. What is P(x # 1)?c. What is P(2 # x)? (Hint: Make use of
7.46 Refer to the previous exercise, and suppose that 10 rather than six passengers are selected (n 5 10, p 5 .8). (Hint: Use technology or Appendix Table 9.)a. What is p(8)?b. Calculate P(x # 7).c. Calculate the probability that more than half of the selected passengers rested or slept.
7.45 ▼ The Los Angeles Times (December 13, 1992) reported that what airline passengers like to do most on long flights is rest or sleep. In a survey of 3697 passengers, almost 80% did so. Suppose that for a particular route the actual percentage is exactly 80%, and consider randomly selecting six
7.44 The article “Should You Report That Fender-Bender?”(Consumer Reports, 2013:15) reported that 7 in 10 auto accidents involve a single vehicle. Suppose 15 accidents are randomly selected. (Hint: See Examples 7.19 and 7.20.)a. What is the probability that exactly four involve a single
7.43 NBC News reported that 1 in 20 children in the U.S. has a food allergy (May 2, 2013). Consider selecting 10 children at random. Define the random variable x as x 5 number of children in the sample of 10 that have a food allergy Find the following probabilities. (Hint: See Examples 7.19 and
7.42 The states of Ohio, Iowa, and Idaho are often confused, probably because the names sound so similar.Each year, the State Tourism Directors of these three states drive to a meeting in one of the state capitals to discuss strategies for attracting tourists to their states so that the states will
7.41 Consider a game in which a red die and a blue die are rolled. Let xR denote the value showing on the uppermost face of the red die, and define xB similarly for the blue die.a. The probability distribution of xR is xR 1 2 3 4 5 6 p(xR) 1/6 1/6 1/6 1/6 1/6 1/6 Find the mean, variance, and
7.40 A multiple-choice exam consists of 50 questions.Each question has five choices, of which only one is correct. Suppose that the total score on the exam is computed as y x1 2 14 x2 where x1 5 number of correct responses and x2 5 number of incorrect responses. (Calculating a total score by
7.39 ▼ To assemble a piece of furniture, a wood peg must be inserted into a predrilled hole. Suppose that the diameter of a randomly selected peg is a random variable with mean 0.25 inch and standard deviation 0.006 inch and that the diameter of a randomly selected hole is a random variable with
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