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statistics
essentials of statistics for the behavioral sciences
Introduction To Statistics And Data Analysis 3rd Edition Roxy Peck, Chris Olsen, Jay L. Devore - Solutions
High productivity and carbohydrate storage ability of the Jerusalem artichoke make it a promising agricultural crop. The article “Leaf Gas Exchange and TuberYield in Jerusalem Artichoke Cultivars” (Field Crops Research [1991]: 241–252) reported on various plant characteristics. Consider the
The nutritional quality of shrubs commonly used for feed by rabbits was the focus of a study summarized in the article “Estimation of Browse by Size Classes for Snowshoe Hare” (Journal of Wildlife Management [1980]: 34–40). The energy content (cal/g) of three sizes (4 mm or less, 5–7 mm,
Exercise 5.46 presented data on x = squawfish length and y = maximum size of salmonid consumed, both in mm. Use the accompanying MINITAB output along with the values x̅ = 343.27 and Sxx = 69,112.18 to answer the following questions.a. Does there appear to be a useful linear relationship between
The article “The Caseload Controversy and the Study of Criminal Courts” (Journal of Criminal Law and Criminology [1979]: 89–101) used a multiple regression analysis to help assess the impact of judicial caseload on the processing of criminal court cases. Data were collected in the Chicago
The article “An Analysis of Job Sharing, Full-Time, and Part-Time Arrangements” (American Business Review [1989]: 34–40) reported on a study of hospital employees from three different groups. Each employee reported a level of satisfaction with his or her work schedule (1 = very dissatisfied
The article “Statistical Comparison of Heavy Metal Concentrations in Various Louisiana Sediments” (Environmental Monitoring and Assessment [1984]: 163–170) gave the accompanying data on depth (m), zinc concentration (ppm), and iron concentration (%) for 17 core samples.a. Using a .05
By analogy with the discussion in Exercise 13.46, when two different prediction intervals are computed, each at the 95% prediction level, the simultaneous prediction level is at least [100 − 2(5)]% = 90%.a. Return to Exercise 13.46 and obtain prediction intervals for sunburn index both when
A regression of y = sunburn index for a pea plant on x = distance from an ultraviolet light source was considered in Exercise 13.22. The data and summary statistics presented there givea. Calculate a 95% confidence interval for the true average sunburn index when the distance from the light source
This activity requires the use of a statistical computer package capable of fitting multiple regression models. Background: The given data on y, x1, x2, x3, and x4 were generated using a computer package capable of producing random observations from any specified normal distribution. Because the
Data on x = depth of flooding and y = flood damage were given in Exercise 5.75. Summary quantities area. Do the data suggest the existence of a positive linear relationship (one in which an increase in y tends to be associated with an increase in x)? Test using a .05 significance level.b. Predict
An investigation carried out to study the toxic effects of mercury was described in the article “Comparative Responses of the Action of Different Mercury Compounds on Barley” (International Journal of Environmental Studies [1983]: 323–327). Ten different concentrations of mercury (0, 1, 5,
High blood-lead levels are associated with a number of different health problems. The article “A Study of the Relationship between Blood Lead Levels and Occupational Lead Levels” (American Statistician [1983]: 471) gave data on x = air-lead level (mg/m3) and y = bloodlead level (mg/dL). Summary
The article “Utilizing Feedback and Goal Setting to Increase Performance Skills of Managers” (Academy of Management Journal [1979]: 516–526) reported the results of an experiment to compare three different interviewing techniques for employee evaluations. One method allowed the employee being
The accompanying data on x = U.S. population (millions) and y = crime index (millions) appeared in the article “The Normal Distribution of Crime” (Journal of Police Science and Administration [1975]: 312–318). The author comments that “The simple linear regression analysis remains one of
It has been reported that varying work schedules can lead to a variety of health problems for workers. The article “Nutrient Intake in Day Workers and Shift Workers” (Work and Stress [1994]: 332–342) reported on blood glucose levels (mmol/L) for day-shift workers and workers on two different
If we knew the width and height of cylindrical tin cans of food, could we predict the volume of these cans with precision and accuracy?a. Give the equation that would allow us to make such predictions.b. Is the relationship between volume and its predictors, height and width, a linear one?c. Should
The employee relations manager of a large company was concerned that raises given to employees during a recent period might not have been based strictly on objective performance criteria. A sample of n = 20 employees was selected, and the values of x, a quantitative measure of productivity, and y,
The article “Effects of Gamma Radiation on Juvenile and Mature Cuttings of Quaking Aspen” (Forest Science [1967]: 240–245) reported the following data on x = exposure to radiation (kR/6 hours) and y = dry weight of roots (mg):a. Construct a scatterplot for these data. Does the plot suggest
Exercise 13.8 gave data on x = treadmill run time to exhaustion and y = 20-km ski time. The x values and corresponding standardized residuals from a simple linear regression are as follows.Construct a standardized residual plot. Does the plot exhibit any unusual features?Data from Exercises 13.8The
The article “Root Dentine Transparency: Age Determination of Human Teeth Using Computerized Densitometric Analysis” (American Journal of Physical Anthropology [1991]: 25–30) described a study in which the objective was to predict age (y) from percentage of a tooth’s root with transparent
The article “Effects of Enhanced UV-B Radiation on Ribulose-1,5-Biphosphate, Carboxylase in Pea and Soybean” (Environmental and Experimental Botany [1984]: 131–143) included the accompanying data on pea plants, with y = sunburn index and x = distance (cm) from an ultraviolet light
The Highway Loss Data Institute reported the following repair costs resulting from crash tests conducted in October 2002. The given data are for a 5-mph crash into a flat surface for both a sample of 10 moderately priced midsize cars and a sample of 14 inexpensive midsize cars.a. Compute the
Consider a mediocre basketball player who has consistently made only 50% of his free throws over several seasons. If we were to examine his free throw record over the last 50 free throw attempts, is it likely that we would see a streak of 5 in a row where he is successful in making the free throw?
A college library has four copies of a certain book; the copies are numbered 1, 2, 3, and 4. Two of these are selected at random. The first selected book is placed on 2-hr reserve, and the second book can be checked out overnight.a. Construct a tree diagram to display the 12 outcomes in the sample
An engineering construction firm is currently working on power plants at three different sites. Define events E1, E2, and E3 as follows:E1 = the plant at Site 1 is completed by the contract dateE2 = the plant at Site 2 is completed by the contract dateE3 = the plant at Site 3 is completed by the
Example 4.9 gave 2002 cost-to-charge ratios for inpatient services at 31 hospitals in Oregon. The same data source also provided the cost-to-charge ratios for outpatient services at these same 31 hospitals:a. Use the given data to compute the quartiles and the interquartile range for the outpatient
The following data on degree of exposure to 242Cm alpha particles (x) and the percentage of exposed cells without aberrations (y) appeared in the paper “Chromosome Aberrations Induced in Human Lymphocytes by D-T Neutrons” (Radiation Research [1984]: 561–573):Summary quantities area. Obtain
The following data on x = soil depth (in centimeters) and y = percentage of montmorillonite in the soil were taken from a scatterplot in the paper “Ancient Maya Drained Field Agriculture: Its Possible Application Today in the New River Floodplain, Belize, C.A.” (Agricultural Ecosystems and
The paper “Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River” (Transactions of the American Fisheries Society [1991]: 405–420) gave the following data on y = maximum size of salmonids consumed by a northern squawfish (the most abundant
The article “The Epiphytic Lichen Hypogymnia physodes as a Bioindicator of Atmospheric Nitrogen and Sulphur Deposition in Norway” (Environmental Monitoring and Assessment [1993]: 27–47) gives the following data (read from a graph in the paper) on x = NO3 wet deposition (in grams per cubic
The paper “Crop Improvement for Tropical and Subtropical Australia: Designing Plants for Difficult Climates” (Field Crops Research [1991]: 113–139) gave the following data on x = crop duration (in days) for soybeans and y = crop yield (in tons per hectare):a. Construct a scatterplot of the
The following data on the relationship between degree of exposure to 242Cm alpha radiation particles (x) and the percentage of exposed cells without aberrations (y) appeared in the paper “Chromosome Aberrations Induced in Human Lymphocytes by DT Neutrons” (Radiation Research [1984]:
The article “Characterization of Highway Runoff in Austin, Texas, Area” (Journal of Environmental Engineering [1998]: 131–137) gave a scatterplot, along with the least-squares line for x = rainfall volume (in cubic meters) and y = runoff volume (in cubic meters), for a particular location.
The following data on y = concentration of penicillin-G in pig’s blood plasma (units per milliliter) and x = time (in minutes) from administration of a dose of penicillin (22 mg/kg body weight) appeared in the paper “Calculation of Dosage Regimens of Antimicrobial Drugs for Surgical
The paper cited in Exercise 5.69 gave a scatterplot in which x values were for anterior teeth. Consider the following representative subset of the data:a. Calculate the predicted values and residuals.b. Use the results of Part (a) to obtain SSResid and r2.c. Does the least-squares line appear to
The relationship between the depth of flooding and the amount of flood damage was examined in the paper “Significance of Location in Computing Flood Damage” (Journal of Water Resources Planning and Management [1985]: 65–81). The following data on x = depth of flooding (feet above first-floor
Athletes competing in a triathlon participated in a study described in the paper “Myoglobinemia and Endurance Exercise” (American Journal of Sports Medicine [1984]: 113–118). The following data on finishing time x (in hours) and myoglobin level y (in nanograms per milliliter) were read from a
The paper “Biomechanical Characteristics of the Final Approach Step, Hurdle, and Take-Off of Elite American Springboard Divers” (Journal of Human Movement Studies [1984]: 189–212) gave the following data on y = judge’s score and x = length of final step (in meters) for a sample of seven
The article “Cost-Effectiveness in Public Education” (Chance [1995]: 38–41) reported that for a regression ofy = average SAT score on x = expenditure per pupil, based on data from n = 44 New Jersey school districts, a = 766, b = 0.015, r2 = .160, and se = 53.7.a. One observation in the sample
Consider the chance experiment in which both tennis racket head size and grip size are noted for a randomly selected customer at a particular store. The six possible outcomes (simple events) and their probabilities are displayed in the following table:a. The probability that grip size is 4(1/2) in.
The paper “Root Dentine Transparency: Age Determination of Human Teeth Using Computerized Densitometric Analysis” (American Journal of Physical Anthropology [1991]: 25–30) reported on an investigation of methods for age determination based on tooth characteristics. With y = age (in years) and
Let x denote the amount of gravel sold (in tons) during a randomly selected week at a particular sales facility. Suppose that the density curve has height f(x) above the value x, whereThe density curve (the graph of f(x)) is shown in the following figure:Use the fact that the area of a triangle =
Information from a poll of registered voters in Cedar Rapids, Iowa, to assess voter support for a new school tax was the basis for the following statements (Cedar Rapids Gazette, August 28, 1999):The poll showed 51 percent of the respondents in the Cedar Rapids school district are in favor of the
The paper “What Is the Probability of a Kiss? (It’s Not What You Think)” (Journal of Statistics Education (online) [2002]) posed the following question:What is the probability that a Hershey’s Kiss will land on its base (as opposed to its side) if it is flipped onto a table? Unlike flipping
The New Scientist (January 4, 2002) reported on a controversy surrounding the Euro coins that have been introduced as a common currency across Europe. Each country mints its own coins, but these coins are accepted in any of the countries that have adopted the Euro as their currency.A group in
Consider the chance experiment in which an automobile is selected and both the number of defective headlights (0, 1, or 2) and the number of defective tires (0, 1, 2, 3, or 4) are determined.a. Display possible outcomes using a tree diagram.b. Let A be the event that at most one headlight is
Of the 60 movies reviewed last year by two critics on their joint television show, Critic 1 gave a “thumbs-up” rating to 15, Critic 2 gave this rating to 20, and 10 of the movies were rated thumbs-up by both critics. Suppose that 1 of these 60 movies is randomly selected. a. Given that the
A gas station sells gasoline at the following prices (in cents per gallon, depending on the type of gas and service): 315.9, 318.9, 329.9, 339.9, 344.9, and 359.7. Let y denote the price per gallon paid by a randomly selected customer.a. Is y a discrete random variable? Explain.b. Suppose that the
A Gallup survey of 2002 adults found that 46% of women and 37% of men experience pain daily (San Luis Obispo Tribune, April 6, 2000). Suppose that this information is representative of U.S. adults. If a U.S. adult is selected at random, are the events selected adult is male and selected adult
A shipment of 5000 printed circuit boards contains 40 that are defective. Two boards will be chosen at random, without replacement. Consider the two events E1 = event that the first board selected is defective and E2 = event that the second board selected is defective.a. Are E1 and E2 dependent
A construction firm bids on two different contracts. Let E1 be the event that the bid on the first contract is successful, and define E2 analogously for the second contract. Suppose that P(E1) = .4 and P(E2) = .2 and that E1 and E2 are independent events.a. Calculate the probability that both bids
The article “Birth Beats Long Odds for Leap Year Mom, Baby” (San Luis Obispo Tribune, March 2, 1996) reported that a leap year baby (someone born on February 29) became a leap year mom when she gave birth to a baby on February 29, 1996. The article stated that a hospital spokesperson said that
According to a study released by the federal Substance Abuse and Mental Health Services Administration (Knight Ridder Tribune, September 9, 1999), approximately 8% of all adult full-time workers are drug users and approximately 70% of adult drug users are employed full-time.a. Is it possible for
Ten measurements of the steam rate (in pounds per hour) of a distillation tower were used to construct the following normal probability plot (“A Self-Descaling Distillation Tower,” Chemical Engineering Process [1968]: 79–84). Based on the plot, do you think it is reasonable to assume that the
A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 40% of the cameras sold have been the basic model. Of those buying the basic model, 30% purchase an extended warranty, whereas 50% of all purchasers of the deluxe model buy an extended warranty.
At a large university, the Statistics Department has tried a different text during each of the last three quarters. During the fall quarter, 500 students used a book by Professor Mean; during the winter quarter, 300 students used a book by Professor Median; and during the spring quarter, 200
Only 0.1% of the individuals in a certain population have a particular disease (an incidence rate of .001). Of those who have the disease, 95% test positive when a certain diagnostic test is applied. Of those who do not have the disease, 90% test negative when the test is applied. Suppose that an
A student has a box containing 25 computer disks, of which 15 are blank and 10 are not. She randomly selects disks one by one and examines each one, terminating the process only when she finds a blank disk. What is the probability that she must examine at least two disks?
The recipe calls for four fresh eggs for each quiche. A Salt Lake County Health Department inspector paid a visit recently and pointed out that research by the Food and Drug Administration indicates that one in four eggs carries salmonella bacterium, so restaurants should never use more than three
Consider two binomial experiments.a. The first binomial experiment consists of six trials. How many outcomes have exactly one success, and what are these outcomes?b. The second binomial experiment consists of 20 trials. How many outcomes have exactly 10 successes? exactly 15 successes? exactly 5
A coin is spun 25 times. Let x be the number of spins 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 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 π be the proportion of all residences that have a detector. A random sample of
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).The variable under study was the amount of cadmium in North Atlantic scallops. Do the sample data
The following observations are DDT concentrations in the blood of 20 people:Use the normal scores from Exercise 7.84 to construct a normal probability plot, and comment on the appropriateness of a normal probability model.Data from Exercises 84The paper “The Load-Life Relationship for M50
In a study of warp breakage during the weaving of fabric (Technometrics [1982]: 63), 100 pieces of yarn were tested. The number of cycles of strain to breakage was recorded for each yarn sample. The resulting data are given in the following table:a. Construct a frequency distribution using the
Accurate labeling of packaged meat is difficult because of weight decrease resulting from moisture loss (defined as a percentage of the package’s original net weight). Suppose that moisture loss for a package of chicken breasts is normally distributed with mean value 4.0% and standard deviation
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
Bob 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 number
A sporting goods store has a special sale on three brands of tennis balls—call them D, P, and W. Because the sale price is so low, only one can of balls will be sold to each customer. If 40% of all customers buy Brand W, 35% buy Brand P, and 25% buy Brand D and if x is the number among three
Explain the difference between a population characteristic and a statistic.
According to the article “First-Year Academic Success: A Prediction Combining Cognitive and Psychosocial Variables for Caucasian and African American Students” (Journal of College Student Development [1999]: 599– 605), there is a mild correlation between high school GPA (x) and first-year
Data on high school GPA (x) and first-year college GPA (y) collected from a southeastern public research university can be summarized as follows (“First-Year Academic Success: A Prediction Combining Cognitive and Psychosocial Variables for Caucasian and African American Students,” Journal of
Peak heart rate (beats per minute) was determined both during a shuttle run and during a 300-yard run for a sample of n ! 10 individuals with Down syndrome (“Heart Rate Responses to Two Field Exercise Tests by Adolescents and Young Adults with Down Syndrome,” Adapted Physical Activity Quarterly
Each individual in a sample was asked to indicate on a quantitative scale how willing he or she was to spend money on the environment and also how strongly he or she believed in God (“Religion and Attitudes Toward the Environment,” Journal for the Scientific Study of Religion [1993]: 19–28).
A large bowl of dried beans (or marbles, plastic beads, or any other small, fairly regular objects) and a coin. In this activity, you will investigate whether people can hold more in the right hand or in the left hand.1. Flip a coin to determine which hand you will measure first. If the coin lands
Cost-to-charge ratios (see Example 4.9 for a definition of this ratio) were reported for the 10 hospitals in California with the lowest ratios (San Luis Obispo Tribune, December 15, 2002). These ratios represent the 10 hospitals with the highest markup, because for these hospitals, the actual cost
Disparities among welfare payments by different states have been the source of much political controversy. The accompanying table reports average payment per person (in dollars) in the Aid to Families with Dependent Children Program for the 1990 fiscal year. Construct a relative frequency
A number of studies concerning muscular efficiency in humans have used competitive cyclists as subjects. It had previously been observed that variation in efficiency could not be explained by differences in cycling technique. The paper “Cycling Efficiency Is Related to the Percentage of Type I
USA Today (July 2, 2001) gave the following information regarding cell phone use for men and women:a. Construct a relative frequency histogram for average number of minutes used per month for men. How would you describe the shape of this histogram?b. Construct a relative frequency histogram for
Each student in a sample of 227 boys and 251 girls was asked what he or she thought was most important: getting good grades, being popular, or being good at sports. The resulting data, from the paper “The Role of Sport as a Social Determinant for Children” (Research Quarterly for Exercise and
The clearness index was determined for the skies over Baghdad for each of the 365 days during a particular year (“Contribution to the Study of the Solar Radiation Climate of the Baghdad Environment,” Solar Energy [1990]: 7–12). The accompanying table summarizes the resulting data:a. Determine
The same poll described in Exercise 3.52 also asked the question, “What about salaries? These days, if a man and a woman are doing the same work, do you think the man generally earns more, the woman generally earns more, or that both earn the same amount?” The resulting data are shown in the
In this activity, you will work in groups to collect data that will provide information about how many hours per week, on average, students at your school spend engaged in a particular activity. You will use the sampling plan designed in Activity 2.1 to collect the data.1. With your group, pick one
Stress can affect the physiology and behavior of animals, just as it can with humans (as many of us know all too well). The accompanying data on x ! plasma cortisol concentration (in milligrams of cortisol per milliliter of plasma) and y ! oxygen consumption rate (in milligrams per kilogram per
The article “The Healthy Kids Survey: A Look at the Findings” (San Luis Obispo Tribune, October 25, 2002) gave the accompanying information for a sample of fifth graders in San Luis Obispo County. Responses are to the question:“After school, are you home alone without adult supervision?”a.
Each observation in the following data set is the number of housing units (homes or condominiums) sold during November 1992 in a region corresponding to a particular Orange County, California, ZIP code:Construct a stem-and-leaf display, and comment on any interesting features. 25 18 16 6 26 11 29 7
The web site PollingReport.com gave data from a CBS news poll conducted in December 1999. In the survey described, people were asked the following question: “All things considered, in our society today, do you think there are more advantages in being a man, more advantages in being a woman, or
The Highway Loss Data Institute publishes data on repair costs resulting from a 5-mph crash test of a car moving forward into a flat barrier. The following table gives data for 10 midsize luxury cars tested in October 2002:Compute the values of the mean and the median. Why are these values so
In this activity, you will investigate the relationship between boxplot shapes and the corresponding five-number summary. The accompanying figure shows four boxplots, labeled A–D. Also given are four five-number summaries, labeled I–IV. Match each five-number summary to the appropriate boxplot.
A sample of n = 5 college students yielded the following observations on number of traffic citations for a moving violation during the previous year:Calculate s2 and s. xs = 2 = = 3 X4 0 = Ex 0 = ²x I = '¹x
The following data values are 1989 per capita expenditures on public libraries for each of the 50 states:a. Summarize this data set with a frequency distribution. Construct the corresponding histogram.b. Use the histogram in Part (a) to find approximate values of the following percentiles:i.
Open the applet (available in ThomsonNOW at www .thomsonedu.com/login) called CorrelationPoints. You should see a screen like the one shown below.1. Using the mouse, you can click to add points to form a scatterplot. The value of the correlation coefficient for the data in the plot at any given
Each murder committed in Utah during the period 1978–1990 was categorized by day of the week, resulting in the following frequencies: Sunday, 109; Monday, 73; Tuesday, 97; Wednesday, 95; Thursday, 83; Friday, 107; Saturday, 100.a. Construct the corresponding frequency distribution.b. What
The article “Airlines Should Weigh Passengers, Bags, NTSB Says” (USA Today , February 27, 2004) states that the National Transportation Safety Board recommended that airlines weigh passengers and their bags to prevent overloaded planes from attempting to take off. This recommendation was the
To understand better the effects of exercise and aging on various circulatory functions, the article “Cardiac Output in Male Middle-Aged Runners” (Journal of Sports Medicine [1982]: 17–22) presented data from a study of 21 middle-aged male runners. The following data set gives values of
The San Luis Obispo Telegram-Tribune (November 29, 1995) reported the values of the mean and median salary for major league baseball players for 1995. The values reported were $1,110,766 and $275,000.a. Which of the two given values do you think is the mean and which is the median? Explain your
The paper “Increased Vital and Total Lung Capacities in Tibetan Compared to Han Residents of Lhasa” (American Journal of Physical Anthropology [1991]: 341–351) included a scatterplot of vital capacity (y) versus chest circumference (x) for a sample of 16 Tibetan natives, from which the
The paper “Postmortem Changes in Strength of Gastropod Shells” (Paleobiology [1992]: 367–377) included scatterplots of data on x = shell height (in centimeters) and y = breaking strength (in newtons) for a sample of n = 38 hermit crab shells. The least-squares line wasa. What are the slope
The National Survey on Drug Use and Health, conducted in 2002 and 2003 by the Office of Applied Studies, led to the following state estimates of the total number of people (ages 12 and older) who had smoked within the last month).a. Construct a stem-and-leaf display using hundreds (of thousands) as
A newspaper article bemoaning the state of students’ knowledge of geography claimed that more students could identify the island where the 2002 season of the TV show Survivor was filmed than could locate Vermont on a map of the United States. In this activity, you will collect data that will
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