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statistics for engineers and scientists
A First Course In Statistics 12th Edition James T McClave, Terry T Sincich - Solutions
Specify the rejection region for the Wilcoxon rank sum test for independent samples in each of the following situations:a. H0: Two probability distributions, 1 and 2, are identical Ha: The probability distribution for population 1 is shifted to the right or left of the probability distribution for
What conditions are required for a valid application of the Wilcoxon rank sum test?Learning the Mechanics
True or False. If the rank sum for sample 1 is much larger than the rank sum for sample 2 when n1 = n2, then the distribution of population 1 is likely to be shifted to the right of the distribution of population 2.
What is a rank sum?
Scouting an NFL free agent. In seeking a free-agent NFL running back, a general manager is looking for a player with high mean yards gained per carry and a small standard deviation. Suppose the GM wishes to compare the mean yards gained per carry for two free agents, on the basis of independent
Do video game players have superior visual attention skills? Refer to the Journal of Articles in Support of the Null Hypothesis (Vol. 6, 2009) study comparing the visual attention skill of video game and non-video game players, Exercise 7.20 (p. 408). Recall that there was no significant difference
Solar energy generation along highways. Refer to the International Journal of Energy and Environmental Engineering (Dec. 2013) study of solar energy generation along highways, Exercise 7.45 (p. 421). Recall that the researchers compared the mean monthly amount of solar energy generated by east-west
Last name and acquisition timing. Refer to the Journal of Consumer Research (Aug. 2011) study of the last name effect in acquisition timing, Exercise 7.12 (p. 406). Recall that the mean response times (in minutes) to acquire basketball tickets were compared for two groups of MBA students:those
Bulimia study. Refer to the American Statistician (May 2001) study comparing the “fear of negative evaluation”(FNE) scores for bulimic and normal female students, presented in Exercise 7.17 (p. 407). Suppose you want to estimate 1mB - mN2, the difference between the population means of the FNE
Laughter among deaf signers. Refer to the Journal of Deaf Studies and Deaf Education (Fall 2006) paired difference study on vocalized laughter among deaf users of sign language, presented in Exercise 7.42 (p. 420). Suppose you want to estimate md = 1mS - mA2, the difference between the population
Hygiene of handshakes, high fives, and fist bumps. Refer to the American Journal of Infection Control (Aug. 2014) study of the hygiene of hand greetings, Exercise 7.22 (p. 409). The number of bacteria transferred from a gloved hand dipped into a culture of bacteria to a second gloved hand contacted
Enough money has been budgeted to collect independent random samples of size n1 = n2 = 100 from populations 1 and 2 in order to estimate 1p1 - p22. Prior information indicates that p1 = p2 0.4. Have sufficient funds been allocated to construct a 95% confidence interval for 1p1 - p22 of width .1
When will the sample size n1 = n2 = n be the largest, while determining the sample size of estimate of p1 - p2?Learning the Mechanics
When determining the sample size for estimating md , how do you obtain an estimate of the population variance 1sd 22 used in the calculations?
Alcoholic fermentation in wines. Determining alcoholic fermentation in wine is critical to the wine-making process.Must/wine density is a good indicator of the fermentation point, since the density value decreases as sugars are converted into alcohol. For decades, winemakers have measured must/wine
Impact of red light cameras on car crashes. To combat redlight-running crashes, many states are adopting photo-red enforcement programs. In these programs, red light cameras installed at dangerous intersections photograph the license plates of vehicles that run the red light. How effective are
Ethical sensitivity of teachers toward racial intolerance.Many high schools have education programs that encourage teachers to embrace racial tolerance. To gauge the effectiveness of one such program that utilizes two videos of teachers engaging in racial stereotypes of their students, researchers
Linking dementia and leisure activities. Does participation in leisure activities in your youth reduce the risk of Alzheimer’s disease and other forms of dementia? To answer this question, a group of university researchers studied a sample of 107 same-sex Swedish pairs of twins(Journal of
Visual search and memory study. In searching for an item(e.g., a roadside traffic sign, a lost earring, or a tumor in a mammogram), common sense dictates that you will not reexamine items previously rejected. However, researchers at Harvard Medical School found that a visual search has no memory
Acidity of mouthwash. Acid has been found to be a primary cause of dental caries (cavities). It is theorized that oral mouthwashes contribute to the development of caries due to the antiseptic agent oxidizing into acid over time. This theory was tested in the Journal of Dentistry, Oral Medicine and
Estimating well scale deposits. Scale deposits can cause a serious reduction in the flow performance of a well.A study published in the Journal of Petroleum and Gas Engineering (Apr. 2013) compared two methods of estimating the damage from scale deposits (called skin factor).One method of
Solar energy generation along highways. The potential of using solar panels constructed above national highways to generate energy was explored in the International Journal of Energy and Environmental Engineering (Dec.2013). Two-layer solar panels (with 1 meter separating the panels) were
Settlement of shallow foundations. Structures built on a shallow foundation (e.g., a concrete slab-on-grade foundation)are susceptible to settlement. Consequently, accurate settlement prediction is essential in the design of the foundation. Several methods for predicting settlement of shallow
The placebo effect and pain. According to research published in Science (Feb. 20, 2004), the mere belief that you are receiving an effective treatment for pain can reduce the pain you actually feel. Researchers tested this placebo effect on 24 volunteers as follows: Each volunteer was put inside a
Laughter among deaf signers. The Journal of Deaf Studies and Deaf Education (Fall 2006) published an article on vocalized laughter among deaf users of American Sign Language (ASL). In videotaped ASL conversations among deaf participants, 28 laughed at least once. The researchers wanted to know if
Healing potential of handling museum objects. Does handling a museum object have a positive impact on a sick patient’s well-being? To answer this question, researchers at the University College London collected data from 32 sessions with hospital patients (Museum & Society, Nov.2009). Each
Twinned drill holes. A traditional method of verifying mineralization grades in mining is to drill twinned holes, i.e., the drilling of a new hole, or “twin,” next to an earlier drillhole. The use of twinned drill holes was investigated in Exploration and Mining Geology (Vol. 18,
Packaging of a children’s health food. Refer to the Journal of Consumer Behaviour (Vol. 10, 2011) study of packaging of a children’s health food product, Exercise 8.42 (p. 415). Recall that a fictitious brand of a healthy food product—sliced apples—was packaged to appeal to children (a
Summer weight-loss camp. Camp Jump Start is an 8-week summer camp for overweight and obese adolescents.Counselors develop a weight-management program for each camper that centers on nutrition education and physical activity. In a study published in Pediatrics(Apr. 2010), the body mass index (BMI)
A paired difference experiment yielded the following results:nd = 49, xd = 13, sd = 6.a. Test H0: md = 10 against Ha: md 10, where md = 1m1 - m22. Use a = .05.b. Report the p-value for the test you conducted in part a.Interpret the p-value.Applying the Concepts—Basic
The data for a random sample of 10 paired observations are shown in the following table.Pair Population 1 Population 2 1 19 24 2 25 27 3 31 36 4 52 53 5 49 55 6 34 34 7 59 66 8 47 51 9 17 20 10 51 55a. If you wish to test whether these data are sufficient to indicate that the mean for population 2
The data for a random sample of six paired observations are shown in the following table.Pair Sample from Population 1 Sample from Population 2 1 7 4 2 3 1 3 9 7 4 6 2 5 4 4 6 8 7a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1.Use the
A paired difference experiment produced the following data:nd = 9 x1 = 150 x2 = 157 xd = -7 sd 2 = 36a. Determine the values of t for which the null hypothesis m1 - m2 = 0 would be rejected in favor of the alternative hypothesis m1 - m2 6 0. Use a = .10.b. Conduct the paired difference test
Is a paired difference experiment always superior to an independent samples experiment?Learning the Mechanics
Mineral flotation in water study. Refer to the Minerals Engineering (Vol. 46–47, 2013) study of the impact of calcium and gypsum on the flotation properties of silica in water, Exercise 2.48 (p. 77). Fifty solutions of deionized water were prepared both with and without calcium/gypsum, and the
Ethnicity and pain perception. An investigation of ethnic differences in reports of pain perception was presented at the annual meeting of the American Psychosomatic Society (Mar. 2001). A sample of 55 blacks and 159 whites participated in the study. Subjects rated (on a 13-point scale) the
Service without a smile. Although “service with a smile”is a slogan that many businesses adhere to, there are some jobs (e.g., judges, law enforcement officers, pollsters) that require neutrality. An organization will typically provide“display rules” to guide employees on what emotions they
Masculinity and crime. The Journal of Sociology (July 2003) published a study on the link between the level of masculinity and criminal behavior in men. Using a sample of newly incarcerated men in Nebraska, the researcher identified 1,171 violent events and 532 events in which violence was avoided
Does rudeness really matter in the workplace? A study in the Academy of Management Journal (Oct. 2007) investigated how rude behaviors influence a victim’s task performance.College students enrolled in a management course were randomly assigned to one of two experimental conditions:rudeness
How do you choose to argue? In Thinking and Reasoning (Apr. 2007), researchers at Columbia University conducted a series of studies to assess the cognitive skills required for successful arguments. One study focused on whether one would choose to argue by weakening the opposing position or by
Hygiene of handshakes, high five and fist bumps. Health professionals warn that transmission of infectious diseases may occur during the traditional handshake greeting. Two alternative methods of greeting (popularized in sports) are the “high five” and the “fist bump.”Researchers compared
Drug content assessment. Refer to Exercise 4.116 (p. 239)and the Analytical Chemistry (Dec. 15, 2009) study in which scientists used high-performance liquid chromatography to determine the amount of drug in a tablet. Twenty-five tablets were produced at each of two different, independent Site 1
Do video game players have superior visual attention skills? Researchers at Griffin University (Australia) conducted a study to determine whether video game players have superior visual attention skills compared to nonvideo game players (Journal of Articles in Support of the Null Hypothesis, Vol.
Shopping vehicle and judgment. Refer to the Journal of Marketing Research (Dec. 2011) study of shopping cart design, Exercise 2.111 (p. 102). Design engineers want to know whether you may be more likely to purchase a vice product (e.g., a candy bar) when your arm is flexed (as when carrying a
Lobster trap placement. Refer to the Bulletin of Marine Science(Apr. 2010) study of lobster trap placement, Exercise 5.41(p. 297). Recall that the variable of interest was the average distance separating traps—called trap spacing— deployed by teams of fishermen fishing for the red spiny lobster
Bulimia study. The “fear of negative evaluation” (FNE)scores for 11 female students known to suffer from the eating disorder bulimia and 14 female students with normal eating habits, first presented in Exercise 2.44 (p. 76), are reproduced in the next table. (Recall that the higher the score,
Comparing taste test rating protocols. Taste testers of new food products are presented with several competing food samples and asked to rate the taste of each on a 9-point scale(where 1 = “dislike extremely” and 9 = “like extremely”).In the Journal of Sensory Studies (June 2014), food
Children’s recall of TV ads. Children’s recall and recognition of television advertisements was studied in the Journal of Advertising (Spring 2006). Two groups of children were shown a 60-second commercial for Sunkist FunFruit Rock-n-Roll Shapes. One group (the A/V group) was shown the ad with
Cognitive impairment of schizophrenics. A study of the differences in cognitive function between normal individuals and patients diagnosed with schizophrenia was published in the American Journal of Psychiatry (Apr. 2010).The total time (in minutes) a subject spent on the Trail Making Test (a
Effectiveness of teaching software. The U.S. Department of Education (DOE) conducted a national study of the effectiveness of educational software. In one phase of the study, a sample of 1,516 first-grade students in classrooms that used educational software was compared to a sample of 1,103
Last name and acquisition timing. The speed with which consumers decide to purchase a product was investigated in the Journal of Consumer Research (Aug. 2011). The researchers theorized that consumers with last names that begin with letters later in the alphabet will tend to acquire items faster
Shared leadership in airplane crews. Human Factors(Mar. 2014) published a study that examined the effect of shared leadership by the cockpit and cabin crews of a commercial airplane. Simulated flights were taken by 84 six-person crews, where each crew consisted of a twoperson cockpit (captain and
Two independent random samples have been selected, 100 observations from population 1 and 100 from population 2.Sample means x1 = 60 and x2 = 40 were obtained. From previous experience with these populations, it is known that the variances are s1 2 = 64 and s2 2 = 100.a. Find s1x1 - x22.b. Sketch
Independent random samples from normal populations produced the following results:Sample 1 Sample 2 1.2 4.2 3.1 2.7 1.7 3.6 2.8 3.9 3.0a. Calculate the pooled estimate of s2.b. Do the data provide sufficient evidence to indicate that m2 7 m1? Test, using a = .10.c. Find a 90% confidence interval
Assume that s1 2 = s2 2 = s2. Calculate the pooled estimator of s2 for each of the following cases:a. s1 2 = 180, s2 2 = 200, n1 = n2 = 25b. s1 2 = 25, s2 2 = 40, n1 = 10, n2 = 20c. s1 2 = .25, s2 2 = .32, n1 = 8, n2 = 12d. s1 2 = 2300, s2 2 = 2000, n1 = 15, n2 = 18e. Note that the pooled estimate
Independent random samples of 100 observations each are chosen from two normal populations with the following means and standard deviations:Population 1 Population 2 m1 = 16 m2 = 12 s1 = 5 s2 = 4a. Give the mean and standard deviation of the sampling distribution of x1.b. Give the mean and standard
In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:Sample 1 Sample 2 x1 = 5,275 x2 = 5,240 s1 = 150 s2 = 200a. Use a 95% confidence interval to estimate the difference between the population
A confidence interval for 1m1 - m22 is 1 -12, -62. Which of the following inferences is correct?a. m1 7 m2b. m1 6 m2c. m1 = m2d. no significant difference between means Learning the Mechanics
Two populations are described in each of the cases that follow.In which cases would it be appropriate to apply the small-sample t-test to investigate the difference between the population means?Exercises 7.1–7.28a. Population 1: Normal distribution with variance s1 2 ; Population 2: Skewed to the
Parents who condone spanking. In Exercise 4.188 (p. 265)you read about a nationwide survey that claimed that 60%of parents with young children condone spanking their child as a regular form of punishment (Tampa Tribune, Oct. 5, 2000). In a random sample of 100 parents with young children, how many
Study of lunar soil. Meteoritics (Mar. 1995) reported the results of a study of lunar soil evolution. Data were obtained from the Apollo 16 mission to the moon, during which a 62-cm core was extracted from the soil near the landing site.Monomineralic grains of lunar soil were separated out and
Alkalinity of river water. The median alkalinity level of water specimens collected from the Han River in Seoul, South Korea, is 50 milligrams per liter (Environmental Science & Engineering, Sept. 1, 2000). Consider a random sample of 10 water specimens collected from a tributary of the Han River.
Free recall memory strategy. Refer to the Advances in Cognitive Psychology (Oct. 2012) study of free recall memory, Exercise 6.67 (p. 361). Recall that each in a sample of 8 participants memorized a list of items using the category clustering strategy and the ratio of repetition was recorded for
Crab spiders hiding on flowers. Refer to the Behavioral Ecology (Jan. 2005) field study on the natural camouflage of crab spiders, presented in Exercise 2.42 (p. 75).Ecologists collected a sample of 10 adult female crab spiders, each sitting on the yellow central part of a daisy, and measured the
Music performance anxiety. Refer to the British Journal of Music Education (Mar. 2014) study of performance anxiety by music students, Exercise 6.60 (p. 359). Recall that the Performance Anxiety Inventory (PAI) was used to measure music performance anxiety on a scale from 20 to 80 points.The table
Use Table I of Appendix B or statistical software to calculate the following binomial probabilities:a. P1x Ú 42 when n = 6 and p = .4b. P1x Ú 72 when n = 8 and p = .4c. P1x Ú 52 when n = 5 and p = .4d. P1x Ú 142 when n = 2 and p = .4. Also, use the normal approximation to calculate this
Motivation of drug dealers. Refer to the Applied Psychology in Criminal Justice (Sept. 2009) study of the personality characteristics of convicted drug dealers, Exercise 5.17 (p. 286). A random sample of 100 drug dealers had a mean Wanting Recognition (WR) score of 39 points, with a standard
Shaft graves in ancient Greece. Refer to the American Journal of Archaeology (Jan. 2014) study of sword shaft graves in ancient Greece, Exercise 2.37 (p. 74). The number of sword shafts buried at each of 13 recently discovered grave sites is reproduced in the following table. Let s represent the
Characteristics of a rockfall. Refer to the Environmental Geology (Vol. 58, 2009) simulation study of how far a block from a collapsing rockwall 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.
Trading skills of institutional investors. The Journal of Finance (Apr. 2011) published the results of an analysis of trading skills of institutional investors. The study focused on “round-trip” trades, i.e., trades in which the same stock was both bought and sold in the same quarter. In a
Astronomy students and the Big Bang Theory. Indiana University professors investigated first-year college students’knowledge of astronomy (Astronomy Education Review, Vol. 2, 2003). One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 148 freshman
Defensibility of a landscape. Settlers often chose sites to live and build communities in based on the landscape’s defensibility.The defensibility of archaeological sites in the Northwest Pacific was investigated in the Journal of Anthropological Archaeology (Vol. 35, 2014). A defensibility index
Underwater acoustic communication. Refer to the IEEE Journal of Oceanic Engineering (Apr. 2013) study of the characteristics of subcarriers—telecommunication signals carried on top of another—for underwater acoustic communications, Exercise 4.68 (p. 218). Recall that a subcarrier can be
6.5 Use the applet entitled Hypotheses Test for a Proportion to investigate the relationships between the probabilities of Type I and Type II errors occurring at levels .05 and .01. For this exercise, use n = 100, true p = 0.5, and alternative not equal.a. Set null p = .5. What happens to the
Suppose the sample in Exercise 6.76 has produced pn = .74 and we wish to test H0: p = .8 against the alternative Ha: p 6 .8.a. Calculate the value of the z statistic for this test.b. Note that the numerator of the z statistic 1pn - p0 =.74 - .80 = -.062 is the same as for Exercise 6.76.Considering
Walking straight into circles. When people get lost in unfamiliar terrain, do they really walk in circles, as is commonly believed? To answer this question, researchers conducted a field experiment and reported the results in Current Biology (Sept. 29, 2009). Fifteen volunteers were blindfolded and
Radon exposure in Egyptian tombs. Refer to the Radiation Protection Dosimetry (Dec. 2010) study of radon exposure in Egyptian tombs, Exercise 5.39(p. 296). The radon levels—measured in becquerels per cubic meter (Bq/m3)—in the inner chambers of a sample of 12 tombs are listed in the table. For
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)
Dental anxiety study. Refer to the BMC Oral Health(Vol. 9, 2009) study of adults who completed the Dental Anxiety Scale, presented in Exercise 4.85 (p. 231). Recall that scores range from 0 (no anxiety) to 25 (extreme anxiety).Summary statistics for the scores of 15 adults who completed the
Lobster trap placement. Refer to the Bulletin of Marine Science (Apr. 2010) observational study of lobster trap placement by teams fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 5.41 (p. 297). Trap spacing measurements (in meters) for a sample of seven teams of red spiny
A sample of five measurements, randomly selected from a normally distributed population, resulted in the following summary statistics: x = 4.8, s = 1.3.a. Test the null hypothesis that the mean of the population is 6 against the alternative hypothesis, m 6 6. Use a = .05.b. Test the null hypothesis
Instructing English-as-a-first-language learners. A study published in the journal Applied Linguistics (Feb. 2014)investigated the effects of implicit and explicit classroom interventions during the instruction of Japanese to Englishas-a-first-language (EFL) students. EFL students at a Japanese
Irrelevant speech effects. Refer to the Acoustical Science& Technology (Vol. 35, 2014) study of irrelevant speech effects, Exercise 5.14 (p. 285). Recall that subjects performed a memorization task under two conditions: (1) with irrelevant background speech and (2) in silence. The difference in the
Cooling method for gas turbines. A popular cooling method for a gas turbine engine uses high-pressure inlet fogging. The performance of a sample of 67 gas turbines augmented with high-pressure inlet fogging was investigated in the Journal of Engineering for Gas Turbines and Power (Jan. 2005). One
Bone fossil study. Archeologists have found that humerus bones from the same species of animal tend to have approximately the same length-to-width ratios. It is known that species A exhibits a mean ratio of 8.5. Suppose 41 fossils of humerus bones were unearthed at an archeological site in East
For each « and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected.a. @ = . 05, p-value = . 005b. @ = . 10, p-value = . 03c. @ = . 05, p-value = . 002d. @ = . 01, p-value = . 028e. @ = . 025, p-value = . 50
If a hypothesis test were conducted using a = .05, for which of the following p-values would the null hypothesis be rejected?a. . 07b. . 20c. . 04d. . 001e. . 002f. . 032
Consider a test of H0: m = 5. In each of the following cases, give the rejection region for the test in terms of the z-statistic:a. Ha: m 7 5, a = .10b. Ha: m 7 5, a = .05c. Ha: m 6 5, a = .01d. Ha: m 5, a = 0.10
A sampling dispute goes to court. Sampling of Medicare and Medicaid claims by the federal and state agencies who administer those programs has become common practice to determine whether providers of those services are submitting valid claims. (See the Statistics in Action for this chapter.)The
Scallops, sampling, and the law. Interfaces (Mar.–Apr.1995) discussed the case of a ship that fishes for scallops off the coast of New England. In order to protect baby scallops from being harvested, the U.S. Fisheries and Wildlife Service requires that “the average meat per scallop weigh at
Air bags pose danger for children. By law, all new cars must be equipped with both driver-side and passengerside safety air bags. There is concern, however, over whether air bags pose a danger for children sitting on the passenger side. In a National Highway Traffic Safety Administration (NHTSA)
Latex allergy in health care workers. Refer to the Current Allergy & Clinical Immunology (Mar. 2004) study of health care workers who use latex gloves, presented in Exercise 5.15 (p. 286). In addition to the 46 hospital employees who were diagnosed with a latex allergy on the basis of a skin-prick
Salmonella in ice cream bars (cont’d). Refer to Exercise 5.145. Suppose it is now 1 year after the poisoning was traced to ice cream bars. The manufacturer wishes to estimate the proportion who still will not purchase bars to within .04, using a 90% confidence interval. How many consumers should
Training zoo animals. Refer to Exercise 2.193 (p. 132) and the Teaching of Psychology (May 1998) study in which students assisted in the training of zoo animals. A sample of 15 psychology students rated “The Training Game” as a “great”method of understanding the animal’s perspective
Studies on treating Alzheimer’s disease. Alzheimer’s disease is a progressive disease of the brain. The journal eCAM (Nov. 2006) published an article that critiqued the quality of the methodology used in studies on Alzheimer’s treatment. For each in a sample of 13 studies, the quality of the
Research on brain specimens. In Exercise 2.45 (p. 76), you learned that the postmortem interval (PMI) is the elapsed time between death and the performance of an autopsy on the cadaver. Brain and Language (June 1995) reported on the PMIs of 22 randomly selected human brain specimens obtained at
Scary-movie study. According to a University of Michigan study, many adults have experienced lingering “fright” effects from a scary movie or TV show they saw as a teenager. In a survey of 150 college students, 39 said they still experience“residual anxiety” from a scary TV show or movie.a.
Oven cooking study. A group of Harvard University School of Public Health researchers studied the impact of cooking on the size of indoor air particles (Environmental Science& Technology, Sept. 1, 2000). The decay rate (measured in mm>hour) for fine particles produced from oven cooking or toasting
Attention time given to twins. Psychologists have found that twins, in their early years, tend to have lower IQs and pick up language more slowly than nontwins (Wisconsin Twin Research Newsletter, Winter 2004). The slower intellectual growth of most twins may be caused by benign parental neglect.
Radioactive lichen. Refer to the Lichen Radionuclide Baseline Research project at the University of Alaska, presented in Exercise 2.196 (p. 132). Recall that the researchers collected 9 lichen specimens and measured the amount (in microcuries per milliliter) of the radioactive element cesium-137
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