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essentials of statistics
The Basic Practice Of Statistics 5th Edition David S Moore - Solutions
A political party’s data bank includes the zip codes of past donors, such as 47906 34236 53075 10010 90210 75204 30304 99709 Zip code is a(a) quantitative variable. (b) categorical variable. (c) unit of measurement.
A study of recent college graduates records the sex and total college debt in dollars for 10,000 people a year after they graduate from college.(a) Sex and college debt are both categorical variables.(b) Sex and college debt are both quantitative variables.(c) Sex is a categorical variable and
To display the distribution of grades (A, B, C, D, F) in a course, it would be correct to use(a) a pie chart but not a bar graph.(b) a bar graph but not a pie chart.(c) either a pie chart or a bar graph.
Here are the first lines of a professor’s data set at the end of a statistics course:Name Major Points Grade ADVANI, SURA COMM 397 B BARTON, DAVID HIST 323 C BROWN, ANNETTE BIOL 446 A CHIU, SUN PSYC 405 B CORTEZ, MARIA PSYC 461 A The individuals in these data are (a) the students. (b) the total
Hooded rats: social play counts. In Exercise 28.13 you carried out two-way ANOVA for a study of the effect of social isolation on hooded rats. The response variable is the count of social play episodes during an observation period.Start your work in this exercise with your two-way ANOVA table from
Hooded rats: social play times. In Exercise 28.12 you carried out two-way ANOVA for a study of the effect of social isolation on hooded rats. The response variable is the time (in seconds) that a rat devoted to social play during an observation period. Start your work in this exercise with your
Metabolic rates in caterpillars. Professor Harihuko Itagaki and his students have been measuring metabolic rates in tobacco hornworm caterpillars (Manduca sexta)for years. The researchers do not want the metabolic rates to depend on which analyzer they use to obtain the measurements. They therefore
Hooded rats: social play counts. The researchers who conducted the study ST EP in the previous exercise also recorded the number of times each of three types of behavior (object play, locomotor play, and social play) occurred. The file ex28-13.dat contains the counts of social play episodes by each
Hooded rats: social play times. How does social isolation during a critical development period affect the behavior of hooded rats? Psychology students assigned 24 young female rats at random to either isolated or group housing, then similarly assigned 24 young male rats. This is a randomized block
Working with sample means. A student project measured the increase in the heart rates of fellow students when they stepped up and down for three minutes to the beat of a metronome. The explanatory variables are step height (Lo =5.75 inches, Hi = 11.5 inches) and metronome beat (Slow = 14
Recognizing effects. Consider the mean responses plotted in Figure 28.8(b).(a) Is there an interaction between soybean variety and herbicide type? Why or why not?(b) Is there a main effect of herbicide type? Why or why not?(c) Is there a main effect of soybean variety? Why or why not?
Recognizing effects. Consider the mean responses plotted in Figure 28.8(a).(a) Is there an interaction between soybean variety and herbicide type? Why or why not?(b) Is there a main effect of herbicide type? Why or why not?(c) Is there a main effect of soybean variety? Why or why not?
Logging in the rain forest: contrasts. Figure 28.2 gives basic ANOVA output for the study of the effects of logging described in Example 28.1.We might describe the overall effect of logging by comparing the mean species count for unlogged plots(Group A) with the average of the mean counts for the
Green versus yellow. Using the Minitab output in Figure 28.4, verify the values for the sample contrast ˆL 2 and its standard error given in Example 28.7. Give a 95% confidence interval for the population contrast L2. Carry out a test of the hypothesis H0: L2 = 0 against the two-sided alternative.
Dogs, friends, and stress. In Exercise 28.3, the ANOVA F test had a very small P-value, giving good reason to conclude that mean heart rates under stress do differ depending on whether a pet, a friend, or no one is present. Do the means for the two treatments (pet, friend) differ significantly from
Which color attracts beetles best? Exercise 28.2 presents data on the numbers of cereal leaf beetles trapped by boards of four different colors. Yellow boards appear most effective. ANOVA gives very strong evidence that the colors differ in their ability to attract beetles.(a) How many pairwise
Logging in the rain forest. In Exercise 28.1, you carried out basic ANOVA to compare the mean counts of individual trees in forest plots of types A, B, and C.(a) Find the Tukey simultaneous 95% confidence intervals for all pairwise differences among the three population means.(b) Explain in simple
Dogs, friends, and stress. If you are a dog lover, perhaps having your dog along reduces the effect of stress. To examine the effect of pets in stressful situations, researchers recruited 45 women who said they were dog lovers. The EESEE story“Stress among Pets and Friends” describes the
Which color attracts beetles best? To detect the presence of harmful insects in farm fields, we can put up boards covered with a sticky material and examine the insects trapped on the boards. Which colors attract insects best? Experimenters placed six boards of each of four colors at random
Logging in the rain forest. The full data for the logging study appear in Table 24.2 (text page 640). The data for counts of individual trees in the plots studied also appear in the data file ex28-01.dat. Carry out data analysis and ANOVA to determine whether logging affects the mean count of
The clothing retailer problem. The scatterplot and histogram on page 27-59 show the residuals from the model in Example 27.20 with all explanatory variables, some interaction terms, and quadratic terms. Comment on both plots. Do you see any reason for concern in using this model for inference?
Final model for the clothing retailer problem. The residual plots on page 27-58 show the residuals for the final model in the clothing retailer problem plotted against Purchase12 and Recency. Do the plots suggest any potential problems with the conditions for inference? Comment.
World record running times. Exercise 27.15 (page 27-30) shows the progress of world record times (in seconds) for the 10,000-meter run for both men and women.(a) Provide theANOVAtable for the regression model with two regression lines, one for men and one for women.
Fish sizes. Table 27.8 contains data on the size of perch caught in a lake in Finland.9 Use statistical software to help you analyze these data.(a) Use the multiple regression model with two explanatory variables, length and width, to predict the weight of a perch. Provide the estimated multiple
Tuition and fees at a small liberal arts college. Information regarding tuition and fees at a small liberal arts college from 1951 to 2005, with one exception, is provided in Table 27.7. Use statistical software to answer the following questions.(a) Find the simple linear regression equation for
Diamonds. Suppose that the couple shopping for a diamond in Example 27.15 had used a quadratic regression model for the other quantitative variable, Depth.Use the data in the file ta27-04.dat to answer the following questions.(a) What is the estimated quadratic regression model for mean total price
Combining relationships. Suppose that x1 = 2x2 − 4 so that x1 and x2 are positively correlated. Let y = 3x2 + 4 so that y and x2 are positively correlated.(a) Use the relationship between x1 and x2 to find the linear relationship between y and x1. Are y and x1 positively correlated?(b) Add the
Body fat for men. You are interested in predicting the amount of body fat on a man y using the explanatory variables waist size x1 and height x2.(a) Do you think body fat y and waist size x1 are positively correlated? Explain.(b) For a fixed waist size, height x2 is negatively correlated with body
Predicting SAT verbal scores.We have been developing models for SAT math scores for two different clusters of states. Use the SAT data to evaluate similar models for SAT verbal scores. The file eg27-11.dat contains the data.(a) Find the least-squares line for predicting SAT verbal scores from
Radioactive decay. An experiment was conducted using a Geiger-Mueller tube in a physics lab. Geiger-Mueller tubes respond to gamma rays and to beta particles(electrons). A pulse that corresponds to each detection of a decay product is produced, and these pulses were counted using a computer-based
Diamonds. Specify the population regression model for predicting the total price of a diamond from two interacting variables, Carat and Depth.
Nest humidity and fleas. In the setting of Exercise 27.7 (page 27-14), researchers showed that the square root of the number of adult fleas y has a quadratic relationship with the nest humidity index x. Specify the population regression model for this situation.
Heights and weights for boys and girls. Suppose that you are designing a study to investigate the relationship between height and weight for boys and girls. Specify a model with two regression lines that could be used to predict height separately for boys and for girls. Be sure to identify all
World record running times. The table below shows the progress of world record times (in seconds) for the 10,000-meter run for both men and women.Men Women Record Time Record Time Record Time year (seconds) year (seconds) year (seconds)1912 1880.8 1962 1698.2 1967 2286.4 1921 1840.2 1963 1695.6
Revisiting state SAT scores.We have examined the relationship between SAT math scores and the percent of high school graduates who take the SAT. CrunchIt!was used to fit a model with two regression lines, one for each cluster, for predicting SAT verbal score. Use the CrunchIt! output on page 27-29
Touring battlefields. Suppose that buses complete tours at an average rate of 20 miles per hour and that self-guided cars complete tours at an average rate of 28 miles per hour. Give a regression model that describes how mean time to complete a tour changes with distance x1 and mode of
How fast do icicles grow? We have data on the growth of icicles starting at length 10 centimeters (cm) and at length 20 cm. Suppose that icicles which start at 10 cm grow at a rate of 0.15 cm per minute and icicles which start at 20 cm grow at the same rate, 0.15 cm per minute. Give a regression
Bird colonies. Suppose that the number y of new birds that join a colony this year has a straight-line relationship with the percent x1 of returning birds in colonies of two different bird species. An indicator variable shows which species we observe:x2 = 0 for one and x2 = 1 for the other.Write a
Reporting percents. Use the output in Figure 27.3 to answer the questions below.(a) Is the value of the regression standard error the same on both sets of output?Interpret this value.(b) The value of the squared multiple correlation coefficient is reported as 71.9%by Minitab and 0.7188 by CrunchIt!
Metabolic rate and body mass for caterpillars. Use the output provided in Example 27.10 to answer the questions below.(a) Find a 95% confidence interval for the slope parameter β for caterpillars during Stage 4.(b) If you were asked to report a confidence interval for the slope parameter βfor
Metabolic rate and body mass for caterpillars. Does the general relationship between metabolic rate and body mass described in Example 27.10 hold for tobacco hornworm caterpillars? The Minitab output (see page 27-22) was obtained by regressing the response variable y = log(MR) on x1 = log(BM) for
Nestling mass and nest humidity. Researchers investigated the relationship between nestling mass, measured in grams, and nest humidity index, measured as the ratio of total mass of water in the nest divided by nest dry mass, for two different groups of great titmice parents.2 One group was exposed
Heights and weights for boys and girls. Suppose you are designing a study to investigate the relationship between height and weight for boys and girls.(a) Specify a model with parallel regression lines that could be used to predict height separately for boys and for girls. Be sure to identify all
Potential jurors. Here are descriptive statistics and a scatterplot for the reporting percents in 2003 and 2004 from Table 27.2.(a) Use the descriptive statistics to compute the least-squares regression line for predicting the reporting percent from the coded reporting date in 2003.(b) Use the
Potential jurors. In Example 27.3 the indicator variable for year ( x2 = 0 for 1998 and x2 = 1 for 2000) was used to combine the two separate regression models from Example 27.1 into one multiple regression model. Suppose that instead of x2 we use an indicator variable x3 that reverses the two
Potential jurors. On page 27-9 are descriptive statistics and a scatterplot for the reporting percents in 1985 and 1997 from Table 27.2.(a) Use the descriptive statistics to compute the least-squares regression line for predicting the reporting percent from the coded reporting date in 1985.(b) Use
How fast do icicles grow? We have data on the growth of icicles starting at length 10 centimeters (cm) and at length 20 cm. An icicle grows at the same rate, 0.15 cm per minute, starting from either length. Give a regression model that describes how mean length changes with time x1 and starting
Bird colonies. Suppose (this is too simple to be realistic) that the number y of new birds that join a colony this year has the same straight-line relationship with the percent x1 of returning birds in colonies of two different bird species. An indicator variable shows which species we observe: x2
School absenteeism. Here are data from an urban school district on the number of eighth-grade students with three or more unexcused absences from school during each month of a school year. Because the total number of eighth-graders changes a bit from month to month, these totals are also given for
Aircraft rivets. After completion of an aircraft wing assembly, inspectors count the number of missing or deformed rivets. There are hundreds of rivets in each wing, but the total number varies depending on the aircraft type. Recent data for wings with a total of 34,700 rivets show 208 missing or
Lost baggage. The Department of Transportation reports that about 1 of every 200 passengers on domestic flights of the 10 largest U.S. airlines files a report of mishandled baggage. Starting with this information, you plan to sample records for 1000 passengers per day at a large airport to monitor
Unpaid invoices. The controller’s office of a corporation is concerned that invoices that remain unpaid after 30 days are damaging relations with vendors. To assess the magnitude of the problem, a manager searches payment records for invoices that arrived in the past 10 months. The average number
Setting up a p chart. After inspecting Figure 26.16, you decide to monitor the next four weeks’ absenteeism rates using a center line and control limits calculated from the second two weeks’ data recorded in Table 26.8. Find p for these 10 days and give the new values of CL, LCL, and UCL.
Mounting-hole distances, continued. The record sheet in Figure 26.10 gives the specifications as 0.6054 ± 0.0010 inch. That’s 54 ± 10 as the data are coded on the record sheet. Assuming that the distance varies Normally from meter to meter, about what percent of meters meet the specifications?
Mounting-hole distances. Figure 26.10 (page 26-20) displays a record sheet for 18 samples of distances between mounting holes in an electrical meter. The data file ex26-15.dat adds x and s for each sample. In Exercise 26.15, you found that Sample 5 was out of control on the process-monitoring s
Improving capability. The center of the specifications for mesh tension in the previous exercise is 250 mV, but the center of our process is 275 mV. We can improve capability by adjusting the process to have center 250 mV. This is an easy adjustment that does not change the process variation. What
Describing capability. If the mesh tension of individual monitors follows a Normal distribution, we can describe capability by giving the percent of monitors that meet specifications. The old specifications for mesh tension are 100 to 400 mV.The new specifications are 150 to 350 mV. Because the
Normality? Do the losses on the 120 individual patients in Table 26.6 appear to come from a single Normal distribution? Make a graph and discuss what it shows.Are the natural tolerances you found in the previous exercise trustworthy?
Natural tolerances. Table 26.6 (page 26-28) gives data on hospital losses for samples of DRG 209 patients. The distribution of losses has been stable over time.What are the natural tolerances within which you expect losses on nearly all such patients to fall?
No incoming inspection. The computer makers who buy monitors require that the monitor manufacturer practice statistical process control and submit control charts for verification. This allows the computer makers to eliminate inspection of monitors as they arrive, a considerable cost saving. Explain
The Boston Marathon. The Boston Marathon has been run each year since 1897.Winning times were highly variable in the early years, but control improved as the best runners became more professional. A clear downward trend continued until the 1980s. Rick plans to make a control chart for the winning
A cutting operation. A machine tool in your plant is cutting an outside diameter.A sample of 4 pieces is taken near the end of each hour of production. Table 26.7 gives x and s for the first 21 samples, coded in units of 0.0001 inch from the center of the specifications. The specifications allow a
Hospital losses. Table 26.6 gives data on the losses (in dollars) incurred by a hospital in treating major joint replacement (DRG 209) patients.12 The hospital has taken from its records a random sample of 8 such patients each month for 15 months.(a) Make an s control chart using center lines and
Estimating process parameters. The x and s control charts for the meshtensioning example (Figures 26.4 and 26.7) were based on μ = 275 mV andσ = 43 mV. Table 26.1 gives the 20 most recent samples from this process.(a) Estimate the process μ and σ based on these 20 samples.(b) Your calculations
Fromsetup to monitoring. Suppose that when the chart setup project of Example 26.8 is complete, the points remaining after removing special causes have x = 48.7 and s = 0.92. What are the center line and control limits for the x and s charts you would use to monitor the process going forward?
Mixtures. Here is an artificial situation that illustrates an unusual control chart pattern. Invoices are processed and paid by two clerks, one very experienced and the other newly hired. The experienced clerk processes invoices quickly. The new hire must often refer to a handbook and is much
Special causes. Is each of the following examples of a special cause most likely to first result in (i) one-point-out on the s or R chart, (ii) one-point-out on the x chart, or (iii) a run on the x chart? In each case, briefly explain your reasoning. (a) An etching solution deteriorates as more
Dyeing yarn: special causes. The process described in Exercise 26.14 goes out of control. Investigation finds that a new type of yarn was recently introduced. The pH in the kettles is influenced by both the dye liquor and the yarn. Moreover, on a few occasions a faulty valve on one of the kettles
Mounting-hole distances. Figure 26.10 reproduces a data sheet from the floor of a factory that makes electrical meters.7 The sheet shows measurements on the distance between two mounting holes for 18 samples of size 5. The heading informs us that the measurements are in multiples of 0.0001 inch
Dyeing yarn. The unique colors of the cashmere sweaters your firm makes result from heating undyed yarn in a kettle with a dye liquor. The pH (acidity) of the liquor is critical for regulating dye uptake and hence the final color. There are 5 kettles, all of which receive dye liquor from a common
Tablet hardness. Exercise 26.10 concerns process control data on the hardness of tablets (measured in kilograms) for a pharmaceutical product. Table 26.4 gives data for 20 new samples of size 4, with the x and s for each sample. The process has been in control with mean at the target value μ =
Auto thermostats. In Exercise 26.9 you gave the center line and control limits for an x chart. What are the center line and control limits for an s chart for this process?
Responding to applicants. The personnel department of a large company records a number of performance measures. Among them is the time required to respond to an application for employment, measured from the time the application arrives. Suggest some plausible examples of each of the following.(a)
Tablet hardness. A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each lot of tablets is measured in order to control the compression process. The process has been operating in
Auto thermostats. A maker of auto air conditioners checks a sample of 4 thermostatic controls from each hour’s production. The thermostats are set at 75◦F and then placed in a chamber where the temperature is raised gradually. The temperature at which the thermostat turns on the air conditioner
Common causes, special causes. Each weekday morning, you must get to work or to your first class on time. The time at which you reach work or class varies from day to day, and your planning must allow for this variation. List several common causes of variation in your arrival time. Then list
Common causes, special causes. In Exercise 26.1, you described a process that you know well. What are some sources of common cause variation in this process?What are some special causes that might at times drive the process out of control?
Special causes. Jeannine participates in bicycle road races. She regularly rides 25 kilometers over the same course in training. Her time varies a bit from day to day but is generally stable. Give several examples of special causes that might raise Jeannine’s time on a particular day.
Pareto charts. Continue the study of the process of getting to work or class on time from Exercise 26.2. If you kept good records, you could make a Pareto chart of the reasons (special causes) for late arrivals at work or class. Make a Pareto chart that you think roughly describes your own reasons
Pareto charts. Pareto charts are bar graphs with the bars ordered by height. They Pareto charts are often used to isolate the “vital few” categories on which we should focus our attention. Here is an example. A large medical center, financially pressed by restrictions on reimbursement by
Process measurement. Based on your description of the process in Exercise 26.1, suggest specific variables that you might measure in order to(a) assess the overall quality of the process.(b) gather information on a key step within the process.
Describe a process. Each weekday morning, you must get to work or to your first class on time. Make a flowchart of your daily process for doing this, starting when you wake. Be sure to include the time at which you plan to start each step.
Describe a process. Choose a process that you know well. If you lack experience with actual business or manufacturing processes, choose a personal process such as cooking scrambled eggs or balancing your checkbook. Make a flowchart of the process. Make a cause-and-effect diagram that presents the
Food safety. Example 25.5 describes a study of the attitudes of people attending outdoor fairs about the safety of the food served at such locations. The full data set is stored on the CD and online as the file ex25-16.dat. It contains the responses of 303 people to several questions. The variables
Compressing soil. Farmers know that driving heavy equipment on wet soil com-S TE Ppresses the soil and injures future crops. Table 2.5 (text page 65) gives data on the “penetrability” of the same soil at three levels of compression. Penetrability is a measure of how much resistance plant roots
Does polyester decay? Here are the breaking strengths (in pounds) of strips of ST EP polyester fabric buried in the ground for several lengths of time:8 2 weeks 118 126 126 120 129 4 weeks 130 120 114 126 128 8 weeks 122 136 128 146 140 16 weeks 124 98 110 140 110 Breaking strength is a good
Logging in the rain forest: species richness. Table 24.2 (text page 640) contains data comparing the number of trees and number of tree species in plots of land in a tropical rain forest that had never been logged with similar plots nearby that had been logged 1 year earlier and 8 years earlier.
More rain for California? Exercise 24.30 describes an experiment that examines the effect on plant biomass in plots of California grassland randomly assigned to receive added water in the winter, added water in the spring, or no added water The experiment continued for several years. Here are data
Fungus in the air. The air in poultry-processing plants often contains fungus ST EP spores. Inadequate ventilation can damage the health of the workers. The problem is most serious during the summer. To measure the presence of spores, air samples are pumped to an agar plate, and “colony-forming
Sweetening colas. Cola makers test new recipes for loss of sweetness during storage.Trained tasters rate the sweetness before and after storage. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by 10 tasters for one new cola recipe:2.0 0.4 0.7 2.0 −0.4
Does nature heal best? Exercise 17.33 (text page 464) gives these data on the healing rate (micrometers per hour) for cuts in the hind limbs of 12 newts:Newt 1 2 3 4 5 6 7 8 9 10 11 12 Control limb 36 41 39 42 44 39 39 56 33 20 49 30 Experimental limb 28 31 27 33 33 38 45 25 28 33 47 23 The
Ancient air. Exercise 17.7 (text page 449) reports the following data on the percent of nitrogen in bubbles of ancient air trapped in amber:63.4 65.0 64.4 63.3 54.8 64.5 60.8 49.1 51.0 We wonder if ancient air differs significantly from the present atmosphere, which is 78.1% nitrogen.(a) Graph the
Fighting cancer: Normal approximation. Use the Normal approximation with continuity correction to find the P-value for the test in Exercise 25.19.What do you conclude about the effect of infusing modified cells on the ELISA count?David Sanger Photography/Alamy
W+ versus t. Find the one-sided P-value for the matched pairs t test applied to the tree growth data in Exercise 25.18. The smaller P-value of t relative to W+means that t gives stronger evidence of the effect of carbon dioxide on growth.The t test takes advantage of assuming that the data are
Growing trees faster: Normal approximation. Continue your work from Exercise 25.18. Use the Normal approximation with continuity correction to find the P-value for the signed rank test against the one-sided alternative that trees grow faster with added carbon dioxide. What do you conclude?
Fighting cancer. Lymphocytes (white blood cells) play an important role in defending our bodies against tumors and infections. Can lymphocytes be genetically modified to recognize and destroy cancer cells? In one study of this idea, modified cells were infused into 11 patients with metastatic
Growing trees faster. Exercise 17.37 (text page 465) describes an experiment in which extra carbon dioxide was piped to some plots in a pine forest. Each plot was paired with a nearby control plot left in its natural state. Do trees grow faster with extra carbon dioxide? Here are the average
More on food safety. The data file used in Exercise 25.16 contains 303 rows, one for each of the 303 respondents. Each row contains the responses of one person to several questions. We wonder if people are more concerned about safety of food served at fairs than they are about the safety of food
Food safety in restaurants. Example 25.5 describes a study of the attitudes of ST EP people attending outdoor fairs about the safety of the food served at such locations.The full data set is stored on the CD and online as the file ex25-16.dat. It contains the responses of 303 people to several
Cicadas as fertilizer? Exercise 7.41 (text page 193) gives data from an experi-S TE Pment in which some bellflower plants in a forest were “fertilized”with dead cicadas and other plants were not disturbed. The data record the mass of seeds produced by 39 cicada plants and 33 undisturbed
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