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statistics for engineers and scientists
A First Course In Statistics 12th Edition James T McClave, Terry T Sincich - Solutions
Speed training in football. Refer to The Sport Journal(Winter 2004) study on the effectiveness of a speed-training program for football players, Exercise 5.26 (p. 288). The decreases in 40-yard sprint times (time after training minus time before training) for 38 players are saved in the SPRINT
Scanning errors at Wal-Mart. Refer to the National Institute for Standards and Technology (NIST) study of the accuracy of checkout scanners at Wal-Mart stores in California, presented in Exercise 3.56 (p. 163). NIST sets standards so that no more than 2 of every 100 items scanned through an
Extinct New Zealand birds. Refer to the Evolutionary Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, presented in Exercise 2.108 (p. 102). Suppose you are interested in estimating the mean egg length (in millimeters) for the New Zealand bird
A random sample of 400 measurements is selected from a population, and the sample mean and standard deviation are x = 40.5 and s = 26.0, respectively.a. Use a 99% confidence interval to estimate the mean of the population, m.b. How large a sample would be needed to estimate m to within .5 with 99%
Let t0 represent a particular value of t from Table III of Appendix B. Find the table values such that the following statements are true:a. P(t … t0) = .05, where df = 14b. P(t Ú t0) = .005, where df = 19c. P(t … -t0 or t Ú t0) = .10, where df = 9d. P(t … -t0 or t Ú t0) = .01, where df = 28
In each of the following instances, determine whether you would use a z- or t-statistic (or neither) to form a 99% confidence interval for m; then look up the appropriate z or t value.a. Random sample of size n = 17 from a normal distribution with unknown mean m and standard deviation sb. Random
Phishing attacks to e-mail accounts. Refer to the Chance(Summer 2007) study of an actual phishing attack against an organization, Exercise 4.164 (p. 260). Recall that phishing describes an attempt to extract personal/financial information from unsuspecting people through fraudulent e-mail. The
Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a remedy for coughing, Exercise 2.40 (p. 75).Recall that the 105 ill children in the sample were randomly divided into groups. One group received a dosage of an over-the-counter cough
Lobster trap placement. Refer to the Bulletin of Marine Science (Apr. 2010) study of red spiny lobster trap placement, Exercise 5.41 (p. 297). Trap spacing measurements(in meters) for a sample of seven teams of red spiny lobster fishermen are repeated in the table below. The researchers want to
Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise 5.24 (p. 288). Recall that the data on shell length, measured in centimeters, for 76 captured turtles are saved in the TURTLES file. Use the
Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise 2.38 (p. 74). Recall that the researchers recorded the dentary depth of molars (in millimeters)
Oil content of fried sweet potato chips. The characteristics of sweet potato chips fried at different temperatures were investigated in the Journal of Food Engineering (Sept.2013). A sample of 6 sweet potato slices were fried at 130°using a vacuum fryer. One characteristic of interest to the
Facial structure of CEOs. Refer to the Psychological Science (Vol. 22, 2011) study of a chief executive officer’s facial structure, Exercise 5.21 (p. 287). Recall that the facial width-to-height ratio (WHR) was determined by computer analysis for each in a sample of 55 CEOs at publicly traded
Characteristics of a rockfall. Refer to the Environmental Geology (Vol. 58, 2009) simulation study of how far a block from a collapsing rock wall will bounce down a soil slope, Exercise 2.61 (p. 85). Rebound lengths (in meters)were estimated for 13 rock bounces. The data are repeated in the table.
Corporate sustainability of CPA firms. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 5.18 (p. 286). Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was
A random sample of n = 6 observations from a normal distribution resulted in the data shown in the table.Compute a 95% confidence interval for s2.8 2 3 7 11 6
Refer to Exercise 5.103. For each part, a–d, form a 90%confidence interval for s.
Given the following values of x, s, and n, form a 90% confidence interval for s2.a. x = 21, s = 2.7, n = 50b. x = 1.7, s = 0.04, n = 14c. x = 160, s = 31.7, n = 24d. x = 9.8, s = 1.6, n = 5
How many degrees of freedom are associated with a chisquare sampling distribution for a sample of size n?Learning the Mechanics
Eye shadow, mascara, and nickel allergies. Refer to the Journal of the European Academy of Dermatology and Venereology (June 2010) study of the link between nickel allergies and use of mascara or eye shadow, Exercise 5.73(p. 306). Recall that two groups of women were sampled:one group with cosmetic
Do you think you smell? Refer to the Depression and Anxiety (June 2010) study of patients who suffer from olfactory reference syndrome (ORS), Exercise 5.72(p. 306). Recall that psychiatrists disagree over how prevalent ORS is in the human population. Suppose you want to estimate the true proportion
Bacteria in bottled water. Is the bottled water you drink safe? The Natural Resources Defense Council warns that the bottled water you are drinking may contain more bacteria and other potentially carcinogenic chemicals than are allowed by state and federal regulations. Of the more than 1,000
Study of aircraft bird strikes. Refer to the International Journal for Traffic and Transport Engineering (Vol. 3, 2013) study of aircraft bird strikes at a Nigerian airport, Exercise 5.68 (p. 305). Recall that an air traffic controller wants to estimate the true percentage of aircraft bird strikes
Shopping on Black Friday. Refer to the International Journal of Retail and Distribution Management (Vol. 39, 2011) survey of Black Friday shoppers, Exercise 5.22 (p. 287). One question was “How many hours do you usually spend shopping on Black Friday?”a. How many Black Friday shoppers should be
Pitch memory of amusiacs. Refer to the Advances in Cognitive Psychology (Vol. 6, 2010) study of pitch memory of amusiacs, Exercise 5.45 (p. 297). Recall that diagnosed amusiacs listened to a series of tone pairs and were asked to determine if the tones were the same or different.In the first trial,
Duration of daylight in western Pennsylvania. Refer to the Naval Oceanography Portal data on number of minutes of daylight per day in Sharon, PA, Exercise 5.43 (p. 297). An estimate of the mean number of minutes of daylight per day was obtained using data collected for 12 randomly selected days
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 5.67 (p. 305).Recall that you used a 99% confidence interval to estimate the proportion of all social robots designed with legs but
Suppose you wish to estimate a population mean correct to within .12 with a confidence level of .90. You do not know s2, but you know that the observations will range in value between 36 and 44.a. Find the approximate sample size that will produce the desired accuracy of the estimate. You wish to
If nothing is known about p, .5 can be substituted for p in the sample-size formula for a population proportion. But when this is done, the resulting sample size may be larger than needed. Under what circumstances will using p = .5 in the sample-size formula yield a sample size larger than is
If you wish to estimate a population mean with a sampling distribution error SE = 0.29 using a 95% confidence interval and you know from prior sampling that s2 is approximately equal to 3.8, how many observations would have to be included in your sample?
True or false. For a fixed confidence level 11 - a2, increasing the sampling error SE will lead to a smaller n in determining the sample size.Learning the Mechanics
Eye shadow, mascara, and nickel allergies. Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? This was the question of interest in a
Do you think you smell? If you falsely believe you emit an unpleasant, foul, or offensive body odor, you may suffer from olfactory reference syndrome (ORS). The disorder disables patients, who often isolate themselves and consider suicide. Psychiatrists disagree over how prevalent ORS is in the
Splinting in mountain-climbing accidents. The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting of fractures.In High Altitude Medicine & Biology (Vol. 10, 2009), researchers provided
Characteristics of ice-melt ponds. Refer to the University of Colorado study of ice-melt ponds in the Canadian Arctic, presented in Exercise 2.15 (p. 64). Environmental engineers are using data collected by the National Snow and Ice Data Center to learn how climate affects the sea ice. Data on 504
Teenagers’ use of emoticons in school writing. Due to the popularity of instant messaging and social networking, informal elements such as emoticons (e.g., the symbol “:)”to represent a smile) and abbreviations (e.g., “LOL” for“laughing out loud”) have worked their way into
Study of aircraft bird strikes. As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The International Journal for Traffic and Transport Engineering (Vol. 3, 2013) reported on a study of aircraft bird
Are you really being served red snapper? Refer to the Nature (July 15, 2004) study of fish specimens labeled“red snapper,” presented in Exercise 3.93 (p. 179). Recall that federal law prohibits restaurants from serving a cheaper look-alike variety of fish to customers who order red snapper. In
Paying for music downloads. If you use the Internet, have you ever paid to access or download music? This was one of the questions of interest in a recent Pew Internet and American Life Project Survey (Oct. 2010). Telephone interviews were conducted on a representative sample of 1,003 adults living
A random sample of 50 consumers taste-tested a new snack food. Their responses were coded (0: do not like; 1:like; 2: indifferent) and recorded as follows:1 0 0 1 2 0 1 1 0 0 0 1 0 2 0 2 2 0 0 1 1 0 0 0 0 1 0 2 0 0 0 1 0 0 1 0 0 1 0 1 0 2 0 0 1 1 0 0 0 1a. Use an 80% confidence interval to estimate
For the binomial sample information summarized in each part, indicate whether the sample size is large enough to use the methods of this chapter to construct a confidence interval for p.a. n = 500, pn = .05b. n = 100, pn = .05c. n = 10, pn = .5d. n = 10, pn = .3
A random sample of size n = 169 yielded pn = .65.a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p?Explain.b. Construct a 90% confidence interval for p.c. What assumption is necessary to ensure the validity of this confidence interval?
A random sample of size n = 250 yielded p = .80.a. Is the sample size large enough to use the large sample approximation to construct a confidence interval for p?Explain.b. Construct a 95% confidence interval for p.c. Interpret the 95% confidence interval.d. Explain what is meant by the phrase
5.6 Use the applet entitled Confidence Intervals for a Proportion to investigate the effect of the sample size on the number of confidence intervals that contain the population proportion p for a value of p close to 0 or 1.a. Run the applet several times without clearing for p = .5 and n = 50.
If p is near 0 or 1, how large a sample is needed to employ the large-sample confidence interval procedure?Use the applet entitled Confidence Intervals for a Proportion to investigate the effect of the value of p on the number of confidence intervals that contain the population proportion p for a
Explain the meaning of the phrase “pn is an unbiased estimator of p.”
Describe the sampling distribution of pn on the basis of large samples of size n. That is, give the mean, the standard deviation, and the (approximate) shape of the distribution of pn when large samples of size n are (repeatedly)selected from the binomial distribution with probability p of success.
Study on waking sleepers early. Scientists have discovered increased levels of the hormone adrenocorticotropin in people just before they awake from sleeping (Nature, Jan. 7, 1999). In the study described, 15 subjects were monitored during their sleep after being told that they would be woken at a
Antigens for a parasitic roundworm in birds. Ascaridia galli is a parasitic roundworm that attacks the intestines of birds, especially chickens and turkeys. Scientists are working on a synthetic vaccine (antigen) for the parasite. The success of the vaccine hinges on the characteristics of DNA in
Reproduction of bacteria-infected spider mites. Zoologists in Japan investigated the reproductive traits of spider mites with a bacterial infection (Heredity, Jan. 2007). Male and female pairs of infected spider mites were mated in a laboratory and the number of eggs produced by each female
Minimizing tractor skidding distance. In planning for a new forest road to be used for tree harvesting, planners must select the location that will minimize tractor skidding distance. In the Journal of Forest Engineering (July 1999), researchers wanted to estimate the true mean skidding distance
Shaft graves in ancient Greece. Refer to the American Journal of Archaeology (Jan. 2014) study of shaft graves in ancient Greece, Exercise 2.37 (p. 74). Recall that shaft graves are named for the beautifully decorated sword shafts that are buried along with the bodies. The table on p. 298 gives the
Pitch memory of amusiacs. A team of psychologists and neuroscientists tested the pitch memory of individuals diagnosed with amusia (a disorder that impacts one’s perception of music) and reported their results in Advances in Cognitive Psychology (Vol. 6, 2010). Each in a sample of 17 amusiacs
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study on the current trend in the design of social robots, Exercise 2.7 (p. 62). Recall that in a random sample of social robots obtained through a Web search, 28 were built with wheels.The
Duration of daylight in western Pennsylvania. What area of the United States has the least amount of daylight, on average?Having grown up in western Pennsylvania, co-author Sincich wonders if it is his hometown of Sharon, PA. Data on the number of minutes of daylight per day in Sharon, PA, for 12
Shell lengths of sea turtles. Refer to the Aquatic Biology(Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise 5.24(p. 288). Time-depth recorders were deployed on 6 of the 76 captured turtles. The time-depth recorders allowed the environmentalists to
Rainfall and desert ants. Refer to the Journal of Biogeography (Dec. 2003) study of ants and their habitat in the desert of Central Asia, presented in Exercise 2.68(p. 87). Recall that botanists randomly selected five sites in the Dry Steppe region and six sites in the Gobi Desert where ants were
Radon exposure in Egyptian tombs. Many ancient Egyptian tombs were cut from limestone rock that contained uranium. Since most tombs are not well- ventilated, guards, tour guides, and visitors may be exposed to deadly radon gas. In Radiation Protection Dosimetry (Dec. 2010), a study of radon
The following sample of 16 measurements was selected from a population that is approximately normally distributed:91 80 99 110 95 106 78 121 106 100 97 82 100 83 115 104a. Construct an 80% confidence interval for the population mean.b. Construct a 95% confidence interval for the population mean,
The following random sample was selected from a normal distribution: 4, 6, 3, 5, 9, 3.a. Construct a 90% confidence interval for the population mean m.b. Construct a 95% confidence interval for the population mean m.c. Construct a 99% confidence interval for the population mean m.d. Assume that the
Let t0 be a specific value of t. Use technology or Table III of Appendix B to find t0 values such that the following statements are true:a. P(-t0 6 t 6 t0) = .95, where df = 19b. P(t … t0) = .01, where df = 6c. P(t … -t0 or t Ú t0) = .10, where df = 19d. P(t … -t0 or t Ú t0) = .01, where df
Let t0 be a specific value of t. Use technology or Table III in Appendix B to find t0 values such that following statements are true.a. P(t Ú t0) = .025, where df = 10b. P(t Ú t0) = .01, where df = 18c. P(t … t0) = .005, where df = 7d. P(t … t0) = .05, where df = 14
Suppose you have selected a random sample of n = 7 measurements from a normal distribution. Compare the standard normal z-values with the corresponding t-values if you were forming the following confidence intervals:a. 80% confidence intervalb. 90% confidence intervalc. 95% confidence intervald.
Explain the differences in the sampling distributions of x for large and small samples under the following assumptions:a. The variable of interest, x, is normally distributed.b. Nothing is known about the distribution of the variable x.Applet Exercise 5.3 Use the applet entitled Confidence
State the two problems (and corresponding solutions) that arise with using a small sample to estimate m.
The Raid test kitchen. According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers for S. C.Johnson & Son, Inc. (manufacturers of Raid® and Off®), 5,000 roaches (the expected number in a roach-infested house) were
Study of undergraduate problem drinking. In Alcohol &Alcoholism (Jan./Feb. 2007), psychologists at the University of Pennsylvania compared the levels of alcohol consumption of male and female freshman students. Each student was asked to estimate the amount of alcohol (beer, wine, or liquor) they
Speed training in football. Researchers at Northern Kentucky University designed and tested a speed-training program for junior varsity and varsity high school football players (The Sport Journal, Winter 2004). Each in a sample of 38 high school athletes was timed in a 40-yard sprint prior to the
Colored string preferred by chickens. Animal behaviorists have discovered that the more domestic chickens peck at objects placed in their environment, the healthier the chickens seem to be. White string has been found to be a particularly attractive pecking stimulus. In one experiment, 72 chickens
Shopping on Black Friday. The day after Thanksgiving—called Black Friday—is one of the largest shopping days in the United States. Winthrop University researchers conducted interviews with a sample of 38 women shopping on Black Friday to gauge their shopping habits and reported the results in
Facial structure of CEOs. In Psychological Science (Vol.22, 2011), researchers reported that a chief executive officer’s facial structure can be used to predict a firm’s financial performance. The study involved measuring the facial width-to-height ratio (WHR) for each in a sample of 55 CEOs at
Evaporation from swimming pools. A new formula for estimating the water evaporation from occupied swimming pools was proposed and analyzed in the journal Heating/Piping/Air Conditioning Engineering (Apr. 2013). The key components of the new formula are number of pool occupants, area of pool’s
Albedo of ice melt ponds. Refer to the National Snow and Ice Data Center (NSIDC) collection of data on the albedo, depth, and physical characteristics of ice-melt ponds in the Canadian Arctic, presented in Exercise 2.15(p. 64). Albedo is the ratio of the light reflected by the ice to that received
Corporate sustainability of CPA firms. Corporate sustainability refers to business practices designed around social and environmental considerations. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.105 (p. 101). Recall that the
Motivation of drug dealers. Refer to the Applied Psychology in Criminal Justice (Sept. 2009) study of the personality characteristics of drug dealers, Exercise 2.102(p. 101). Recall that each in a sample of 100 convicted drug dealers was scored on the Wanting Recognition (WR Scale, which provides a
Latex allergy in health care workers. Health care workers who use latex gloves with glove powder may develop a latex allergy. Symptoms of a latex allergy include conjunctivitis, hand eczema, nasal congestion, a skin rash, and shortness of breath. Each in a sample of 46 hospital employees who were
Irrelevant speech effects. Refer to the Acoustical Science & Technology (Vol. 35, 2014) study of irrelevant speech effects, Exercise 2.34 (pp. 49). Recall that subjects performed a memorization task under two conditions:(1) with irrelevant background speech and (2) in silence. The difference in the
Heart rate variability of police officers. The heart rate variability(HRV) of police officers was the subject of research published in the American Journal of Human Biology (Jan.2014). HRV is defined as the variation in the time intervals between heartbeats. A measure of HRV was obtained for each
5.1 Use the applet entitled Confidence Intervals for a Mean (the impact of confidence level) to investigate the situation in Exercise 5.11 further. For this exercise, assume that m = 83.2 is the population mean and s = 6.4 is the population standard deviation.a. Using n = 100 and the normal
The mean and standard deviation of a random sample of n measurements are equal to 33.5 and 3.5, respectively.a. Find a 90% confidence interval for m if n = 144.b. Find a 90% confidence interval for m if n = 576.c. Find the widths of the confidence intervals found in parts a andb. What is the effect
Explain the difference between an interval estimator and a point estimator for m.
Soft-drink bottles. A soft-drink bottler purchases glass bottles from a vendor. The bottles are required to have an internal pressure of at least 150 pounds per square inch(psi). A prospective bottle vendor claims that its production process yields bottles with a mean internal pressure of 157 psi
Levelness of concrete slabs. Geotechnical engineers use water-level “manometer” surveys to assess the levelness of newly constructed concrete slabs. Elevations are typically measured at eight points on the slab; of interest is the maximum differential between elevations. The Journal of
Wear-out of used display panels. Wear-out failure time of electronic components is often assumed to have a normal distribution. Can the normal distribution be applied to the wear-out of used manufactured products, such as colored display panels? A lot of 50 used display panels was purchased by an
Comparison of exam scores: red versus blue exam. Refer to the Teaching Psychology (May 1998) study of how external clues influence performance, presented in Exercise 2.128(p. 106). Recall that two different forms of a midterm psychology examination were given, one printed on blue paper and the
Chickens with fecal contamination. The United States Department of Agriculture (USDA) reports that, under its standard inspection system, one in every 100 slaughtered chickens passes inspection for fecal contamination.In Exercise 3.21 (p. 154), you found the probability that a randomly selected
When to replace a maintenance system. An article in the Journal of Quality of Maintenance Engineering (Vol. 19, 2013) studied the problem of finding the optimal replacement policy for a maintenance system. Consider a system that is tested every 12 hours. The test will determine whether there are
Research on eating disorders. Refer to The American Statistician (May 2001) study of female students who suffer from bulimia, presented in Exercise 2.44 (p. 76). Recall that each student completed a questionnaire from which a“fear of negative evaluation” (FNE) score was produced.(The higher the
Where will you get your next pet? Refer to Exercise 4.134(p. 246), Recal that 50% of pet owners will get their next dog or cat from a shelter (USA Today, May 12, 2010).Now, consider a random sample of 200 pet owners, and let x be the number who will get their next dog or cat from a shelter.a. Find
Improving SAT scores. Refer to the Chance (Winter 2001) study of students who paid a private tutor to help them improve their SAT scores, presented in Exercise 2.197 (p. 132). The table summarizing the changes in both the SAT-Mathematics and SAT-Verbal scores for these students is reproduced here.
NHTSA crash safety tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data for new cars, presented in Exercise 2.190 (p. 131). One of the variables measured is the severity of a driver’s head injury when the car is in a head-on collision with a fixed barrier
Dust mite allergies. A dust mite allergen level that exceeds 2 micrograms per gram 1mg>g2 of dust has been associated with the development of allergies. Consider a random sample of four homes, and let x be the number of homes with a dust mite level that exceeds 2 mg>g. The probability distribution
Married-women study. According to Women’s Day magazine(Jan. 2007), 50% of married women would marry their current husbands again if given the chance. Consider the number x in a random sample of 12 married women who would marry their husbands again. Identify the discrete probability distribution
Tracking missiles with satellite imagery. The Space-Based Infrared System (SBIRS) uses satellite imagery to detect and track missiles (Chance, Summer 2005). The probability that an intruding object (e.g., a missile) will be detected on a flight track by SBIRS is .8. Consider a sample of 20
Use of laughing gas. According to the American Dental Association, 60% of all dentists use nitrous oxide (“laughing gas”) in their practice. If x equals the number of dentists in a random sample of five dentists who use laughing gas in practice, then the probability distribution of x is x 0 1 2
Assume that x is a binomial random variable with n = 100 and p = .5. Use the normal probability distribution to approximate the following probabilities:a. P1x … 482b. P150 … x … 652c. P1x Ú 702d. P155 … x … 582e. P1x = 622f. P1x … 49 or x Ú 722 Apply the Concepts–Basic
The random variable x has a normal distribution with m = 80 and s = 20. Find the following probabilities:a. P1x … 852b. P1x Ú 1202c. P160 … x … 902d. P1x 7 852e. P1x 6 1302f. P1x = 952
Suppose x is a binomial random variable with n = 22 and p = .8.a. Find P1x = 162.b. Find P1x … 182.c. Find P1x 7 182.d. Find P112 … x … 162.e. Find P115 6 x 6 202.f. Find m, s2, and s.g. What is the probability that x is in the interval m { 2s?
Consider the discrete probability distribution shown here:x 5 10 12 14 p1x2 .2 .3 .1 .4a. Calculate m, s2, and s.b. What is P1x 6 122?c. Calculate m { 2s.d. What is the probability that x is in the interval m { 2s?
Hand washing versus hand rubbing. Refer to the British Medical Journal (Aug. 17, 2002) study comparing the effectiveness of hand washing with soap and hand rubbing with alcohol, presented in Exercise 2.107 (p. 102). Health care workers who used hand rubbing had a mean bacterial count of 35 per hand
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