Introduction To The Practice Of Statistics 6th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions

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1.32â•‡ Children with ADHD are randomly divided into two groups.One group is given fish oil supplements, and the other is given a placebo. After six months, their symptoms were assessed to see whether fish oil supplements helped reduce ADHD symptoms better than a placebo.
1.31â•‡ A scientist is interested in studying the effect of eating bananas on athletes’ performance levels. She randomly divides a group of athletes into three groups: one group will eat a banana after 30 minutes of exercise, the second will drink water after exercise, and the third will
1.30â•‡ Pedestrian Fatalitiesâ•‡ In 2008, the National Highway Traffic Safety Administration reported that the number of pedestrian fatalities in Miami-Dade County, Florida, was 65 and that the number in Hillsborough County, Florida, was 45. Can we conclude that pedestrians are safer in
1.29â•‡ Course Enrollment Rates (Example 5) Two sections of statistics are offered, the first at 8 a.m. and the second at 10 a.m.The 8 a.m. section has 25 women, and the 10 a.m. section has 15 women. A student claims this is evidence that women prefer earlier statistics classes than men do.
1.28â•‡ Births and Deathsâ•‡ The following information about the number of births and the number of deaths (in thousands) for certain years is taken from the 2012 World Almanac and Book of Facts.Report the death rate as a percentage of the birth rate, and comment on its trend over time.
1.27â•‡ Marriage Ratesâ•‡ The number of married people in the United States and the total number of adults in the United States (in millions) are provided in the accompanying table for several years.Find the percentage of people married in each of the given years, and describe the trend
1.26â•‡ Population Densityâ•‡ The accompanying table gives the population of the six U.S. states with the largest populations in 2008 and the area of these states. (Source: www.infoplease.com)State Population Area (square miles)Pennsylvania 12,448,279 â•‡ 44,817 Illinois 12,901,563
1.25â•‡ Living with AIDSâ•‡ The table gives the number of people diagnosed with AIDS/HIV in 2010 in the five states with the largest number of cases, as well as the District of Columbia, as reported by the U.S. Centers for Disease Control and Prevention (CDC). It also shows the population
1.24â•‡ 2007 Populationâ•‡ The 2009 World Almanac and Book of Facts reported that in 2007 there were 12,608,000 people age 16 or older who had a “go outside the home” disability and that this was 5.5% of the U.S. population (of this age group). These are people who cannot go outside
1.23â•‡ Population Predictionâ•‡ The 2009 World Almanac and Book of Facts predicted that the United States will have an elderly population (65 and older) of 88,547,000 in the year 2050 and that this will be 20.2% of the population. What is the total predicted U.S. population in 2050?
1.22â•‡ Two-way Table from Dataâ•‡ Make a two-way table from Table 1A, for gender and eye color. Put the labels Male and Female across the top and the labels Brown, Blue, and Hazel on the side, and then tally the data.a. Arrange the data as a two-way table and report how many students are
1.21â•‡ Two-way Table from Dataâ•‡ The first step in finding an association between gender and handedness from among the students in Table 1A (on page 51) is to create a two-way table with these two variables. Make a two-way table with the labels Male and Female across the top and the
1.20â•‡ Right-Handed Peopleâ•‡ Find the frequency, proportion, and percentage of right-handed people in Table 1A on page 51.
1.19â•‡ Womenâ•‡ Find the frequency, proportion, and percentage of women in Table 1A on page 51.
1.18â•‡ Finding and Using Percentagesa. In a class of 465 students, 54% of the students were right-handed.How many right-handed students are there?b. A pharmaceutical company recently hired 182 pharmacy graduates and 94 of them are male. What percentage of these graduates are female?c. A
1.17â•‡ Finding and Using Percentages (Example 4)a. A glass jar contains 17 blue marbles and 25 red marbles. What percentage of the marbles are blue?b. A different glass jar has 430 marbles, and 63% of them are blue. How many blue marbles are in the jar?c. A different glass jar contains 45%
1.16â•‡ Favorite Subjectâ•‡ At a high school, a few eighth grade students were asked which subject they liked more: mathematics or science. The table shows the results for boys and girls.Boys Girls Total Mathematics 55 52 ?Science 67 75 142 Total ? 127 ?a. Figure out the missing totals,
1.15â•‡ Older Siblings (Example 3)â•‡ At a small four-year college, some psychology students were asked whether or not they had at least one older sibling. The table shows the results for men and women and shows some of the totals.Men Women Total Yes, Older S 12 55 ?No Older S 11 39
1.14â•‡ A day at the Spaâ•‡ A sample of working professionals in the age group of 25–30 were questioned to determine how much they would be willing to pay for a day at the spa. The males responded(in dollars): 200, 250, 330, 275, and 300. The female students responded: 300, 350, 250,
1.13â•‡ Meetingsâ•‡ Philip, an employee at an IT firm in Mexico, kept track of the duration of his daily meetings (in minutes) for one week. He also took note of whether the meetings took place in the morning or in the afternoon.Morning meetings: 45, 90, 75, 35, 60, 80 Afternoon meetings:
1.12â•‡ Students’ Heightsâ•‡ The accompanying table gives heights(in centimeters) of students in two statistics classes. One class is labeled “Class A” and the other is labeled “Class B”.a. Is the format for the data set stacked or unstacked?b. If you answered “stacked,”
1.11â•‡ Brain Size (Example 2)â•‡ In 1991, researchers conducted a study on brain size as measured by pixels in a magnetic resonance imagery (MRI) scan. The numbers are in hundreds of thousands of pixels. The data table provides the sizes of the brains and theÂ�gender. (Source:
1.10â•‡ Codingâ•‡ Students with fewer than 12 units in the current term are considered part-time. Create a new categorical variable that classifies each student in Table 1A as full-time (12 or more units) or part-time. Call this variable Full. Report the values in a column in the same
1.9â•‡ Codingâ•‡ Explain why the variable Male, in Table 1A, is categorical, even though its values are numbers. Often, it does not make sense, or is not even possible, to add the values of a categorical variable. Does it make sense for Male? If so, what does the sum represent?
1.8â•‡ Codingâ•‡ Suppose you decided to code handedness using Right-handed as the label for the column. How many ones and how many zeros would there be?
1.7â•‡ Codingâ•‡ Suppose you decided to code eye color using 1 for Brown Eyes and 0 for Not Brown Eyes. What would be the label at the top of the column, and how many ones and zeros would there be?
1.6â•‡ Give an example of another categorical variable we might have recorded for the students whose data are in Table 1A?
1.5â•‡ Give an example of another numerical variable we might have recorded for the students whose data are in Table 1A?
1.4â•‡ Are the following variables, from Table 1A, numerical or categorical?Explain.a. Shoe sizeb. Eye color
1.3â•‡ (Example 1)â•‡ Are the following variables, from Table 1A, numerical or categorical? Explain.a. Handednessb. Age
1.2â•‡ Peopleâ•‡ In Table 1A, there are observations on how many people?
1.1â•‡ Variablesâ•‡ In Table 1A, how many variables are there?
17.89 CHALLENGE Probability of another out-of-control signal. Another out-of-control signal is when two out of three successive points are on the same side of the center line and farther than 2σ/√n from it. Find the probability of this event when the process is in control.
17.88 Probability of an out-of-control signal. There are other out-of-control rules that are sometimes used with x charts. One is “15 points in a row within the 1σ level.” That is, 15 consecutive points fall between μ − σ/√n and μ + σ/√n. This signal suggests either that the value of
17.87 More on the film thickness process. Previously, control of the process was based on categorizing the thickness of each film inspected as satisfactory or not. Steady improvement in process quality has occurred, so that just 15 of the last 5000 films inspected were unsatisfactory.(a) What type
17.86 CHALLENGE Calculating the percent that meet specifications. Examination of individual measurements shows that they are close to Normal. If the process mean is set to the target value, about what percent of films will meet the specifications?
17.85 CHALLENGE Capability of the film thickness process.The specifications call for film thickness 830 ± 25 mm× 10−4.(a) What is the estimate ˆσ of the process standard deviation based on the sample standard deviations(after removing samples 1 and 10)? Estimate the capability ratio Cp and
17.84 Recalculating the x and s charts. Interviews with the operators reveal that in samples 1 and 10 mistakes in operating the interferometer resulted in one high-outlier thickness reading that was clearly incorrect. Recalculate x and s after removing samples 1 and 10. Recalculate UCL for the s
17.83 Constructing the s chart. Calculate control limits for s, make an s chart, and comment on control of short-term process variation.
17.82 Selecting the appropriate control chart and limits. At the present time, about 3 lots out of every 1000 lots of material arriving at a plant site from outside vendors are rejected because they are incorrect. The plant receives about 400 lots per week. As part of an effort to reduce errors in
17.81 More on the choice of control chart. What type of control chart or charts would you use as part of efforts to improve each of the following performance measures in a corporate information systems department? Explain your choices.(a) Computer system availability.(b) Time to respond to requests
17.80 Choice of control chart. What type of control chart or charts would you use as part of efforts to improve each of the following performance measures in a corporate personnel office? Explain your choices.(a) Time to get security clearance.(b) Percent of job offers accepted.(c) Employee
17.79 Constructing a Pareto chart. You manage the customer service operation for a maker of electronic equipment sold to business customers.Traditionally, the most common complaint is that equipment does not operate properly when installed, but attention to manufacturing and installation quality
17.78 Describing a process that is in control. A manager who knows no statistics asks you, “What does it mean to say that a process is in control? Is being in control a guarantee that the quality of the product is good?” Answer these questions in plain language that the manager can understand.
17.77 More on monitoring a high-quality process.Because the manufacturing quality in the previous exercise is so high, the process of writing up orders is the major source of quality problems: the defect rate there is 8000 per million opportunities. The manufacturer processes about 500 orders per
17.76 p chart for a high-quality process. A manufacturer of consumer electronic equipment makes full use not only of statistical process control but of automated testing equipment that efficiently tests all completed products. Data from the testing equipment show that finished products have only
17.75 Calculating the p chart limits for school absenteeism. Here are data from an urban school district on the number of eighth-grade students with 3 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
17.74 Constructing the p chart limits for incorrect or illegible prescriptions. A regional chain of retail pharmacies finds that about 1% of prescriptions it receives from doctors are incorrect or illegible.The chain puts in place a secure online system that doctors’ offices can use to enter
17.73 Constructing a p chart for missing or deformed 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
17.72 More on constructing a p chart for damaged eggs. Refer to Exercise 17.71. Suppose that there are two machine operators, each working 4-hour shifts. The first operator is very skilled and can inspect 500 eggs per hour. The second operator is less experienced and can inspect only 400 eggs per
17.71 Constructing a p chart for damaged eggs. An egg farm wants to monitor the effects of some new handling procedures on the percent of eggs arriving at the packaging center with cracked or broken shells. In the past, roughly 2% of the eggs were damaged. A machine will allow the farm to inspect
17.70 Constructing a p chart for mishandled 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
17.69 Constructing a p chart for 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
17.68 Constructing a p chart for absenteeism. After inspecting Figure 17.23, 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 17.11. Find p for these 10 days and give the new values
17.67 More on interpreting the s chart. Each of the 4 out-of-control values of s in part (a) of the previous exercise is explained by a single outlier, a very long response time to one call in the sample. You can see these outliers in Figure 17.17(b). What are the values of these outliers, and what
17.66 Constructing and interpreting the s chart. Table 17.10 also gives x and s for each of the 50 samples.(a) Make an s chart and check for points out of control.(b) If the s-type cause responsible is found and removed, what would be the new control limits for the s chart? Verify that no points s
17.65 to 17.67 make use of this setting.17.65 Choosing the sample. The 6 calls each shift are chosen at random from all calls received during the shift. Discuss the reasons behind this choice and those behind a choice to time 6 consecutive calls.
17.17(b) on page 17-40. A sample of 6 calls is recorded each shift for quality improvement purposes. The time from the first ring until a representative answers the call is recorded.Table 17.10 gives data for 50 shifts, 300 calls total. Exercises
17.64 CHALLENGE More on “six-sigma quality.” The originators of the “six-sigma quality” idea reasoned as follows. Short-term process variation is described by σ. In the long term, the process mean μ will also vary. Studies show that in most manufacturing processes, ±1.5σ is adequate to
17.63 Cp and “six-sigma.” A process with Cp ≥ 2 is sometimes said to have “six-sigma quality.” Sketch the specification limits and a Normal distribution of individual measurements for such a process when it is properly centered. Explain from your sketch why this is called six-sigma
17.62 CHALLENGE Will these actions help the capability?Based on the results of the previous exercise, you conclude that the capability of the clipmaking process is inadequate. Here are some suggestions for improving the capability of this process. Comment on the usefulness of each action
17.61 Assessing the capability of a metal clip process.You are in charge of a process that makes metal clips. The critical dimension is the opening of a clip, which has specifications 15 ± 0.5 millimeters(mm). The process is monitored by x and s charts based on samples of 5 consecutive clips each
17.60 Calculating capability indexes for the DRG 209 hospital losses. Table 17.7 (page 17-36) gives data on a hospital’s losses for 120 DRG 209 patients, collected as 15 monthly samples of 8 patients each.The process has been in control and losses have a roughly Normal distribution. The hospital
17.59 Estimating capability indexes for the distance between holes. Figure 17.10 (page 17-21) displays a record sheet on which operators have recorded 18 samples of measurements on the distance between two mounting holes on an electrical meter. Sample 5 was out of control on an s chart. We remove
17.58 An alternative estimate for Cpk of the mesh tension process. In Exercise 17.54(b) you foundˆC pk for specifications LSL = 150 and USL = 350 using the standard deviation s = 38.38 for all 80 individual monitors in Table 17.1. Repeat the calculation using the control chart estimateˆσ= s/c4.
17.21 shows the density curve. You can see that the process mean (the balance point of the density curve) is μ = 1/2. The standard deviation turns out to be σ = 0.289. Suppose also that LSL = 1/4 and USL = 3/4.0 height = 1 1FIGURE 17.21 Density curve for the uniform distribution on 0 to 1, for
17.57 Capability of a characteristic with a uniform distribution. Suppose that a quality characteristic has the uniform distribution on 0 to 1. Figure
17.56 Can we improve the capability of the meatpackaging process? Refer to Exercise 17.55. The average weight of each section can be increased(or decreased) by increasing (or decreasing) the time between slices of the machine. Based on the results of the previous exercise, would a change in the
17.55 Capability indexes for the meat-packaging process. Table 17.3 (page 17-19) gives 20 process control samples of the weight of ground beef sections. The lower and upper specifications for the 1-pound sections are 0.94 and 1.10.(a) Using these data, estimate Cp and Cpk for this process.(b) What
17.54 Capability indexes for the mesh tension process, continued. We could improve the performance of the mesh tension process discussed in the previous exercise by making an adjustment that moves the center of the process to μ = 250 mV, the center of the specifications. We should do this even if
17.53 Capability indexes for the mesh tension process.Table 17.1 (page 17-10) gives 20 process control samples of the mesh tension of computer monitors.In Example 17.13, we estimated from these samples that ˆμ = x = 275.065 mV and ˆσ = s = 38.38 mV.(a) The original specifications for mesh
17.52 Interpreting the capability indexes. Sketch Normal curves that represent measurements on products from a process with(a) Cp = 2 and Cpk = 0.00.(b) Cp = 2 and Cpk = 0.75.(c) Cp = 2 and Cpk = 1.50.
17.51 Specification limits versus control limits. The manager you report to is confused by LSL and USL versus LCL and UCL. The notations look similar. Carefully explain the conceptual difference between specification limits for individual measurements and control limits for x.
17.50 Monitoring weight. Joe has recorded his weight, measured at the gym after a workout, for several years. The mean is 162 pounds and the standard deviation is 1.5 pounds, with no signs of lack of control. An injury keeps Joe away from the gym for several months. The data below give his weight,
17.49 CHALLENGE Monitoring the winning time of 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
17.48 CHAL LENGE Deming speaks. The quality guru W.Edwards Deming (1900–1993) taught(among much else) that12(a) “People work in the system. Management creates the system.”(b) “Putting out fires is not improvement. Finding a point out of control, finding the special cause and removing it, is
17.47 CHALLENGE Detecting special cause variation. Is each of the following examples of a special cause most likely to first result in (i) a sudden change in level on the s or R chart, (ii) a sudden change in level on the x chart, or (iii) a gradual drift up or down on the x chart? In each case,
17.46 Control charts for the outside diameter. 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 17.9 gives x and s for the first 21 samples, coded in units of 0.0001 inch from the center of the
17.45 Assessing the Normality of the weight measurements. Do the weights of the 60 individual sections in Table 17.3 appear to come from a single Normal distribution? Make a Normal quantile plot and discuss whether the natural tolerances you found in the previous exercise are trustworthy.
17.44 Determining the natural tolerances for the weight of ground beef. Table 17.3 gives data on the weight of ground beef sections. Since the distribution of weights has been stable, use the data in Table 17.3 to construct the natural tolerances within which you expect almost all the weights to
17.43 Assessing the Normality of the distance between holes. Make a Normal quantile plot of the 85 distances in data file ex17 19 that remain after removing sample 5. How does the plot reflect the limited precision of the measurements (all of which end in 4)? Is there any departure from Normality
17.42 Assessing the Normality of the densitometer measurements. Are the 60 individual measurements in Table 17.8 at least approximately Normal, so that the natural tolerances you calculated in Exercise 17.40 can be trusted? Make a Normal quantile plot (or another graph if your software is limited)
17.41 Determining the percent of meters that meet specifications. The record sheet in Figure 17.10 gives the specifications as 0.6054 ± 0.0010 inch.That’s 54 ± 10 as the data are coded on the record.Assuming that the distance varies Normally from meter to meter, about what percent of meters
17.40 Determining the natural tolerances for the densitometer. Remove any samples in Table 17.8 that your work in Exercise 17.38 showed to be out of control on either chart. Estimate the mean and standard deviation of individual measurements on the phantom. What are the natural tolerances for these
17.39 Determining the natural tolerances for the distance between holes. Figure 17.10 (page 17-21) displays a record sheet for 18 samples of distances between mounting holes in an electrical meter. The data file ex17 19 adds x and s for each sample. In Exercise 17.19, you found that sample 5 was
17.38 Monitoring the calibration of a densitometer.Loss of bone density is a serious health problem for many people, especially older women.Conventional X-rays often fail to detect loss of bone density until the loss reaches 25% or more. New equipment such as the Lunar bone densitometer is much
17.37 Improving the capability of the process. The center of the specifications for mesh tension 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
17.36 The percent of products that meet specifications.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
17.35 Checking the Normality of losses. Do the losses on the 120 individual patients in Table 17.7 appear to come from a single Normal distribution? Make a Normal quantile plot and discuss what it shows.Are the natural tolerances you found in the previous exercise trustworthy?
17.34 Determining the tolerances for losses from DRG 209 patients. Table 17.7 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?
17.33 CHALLENGE Efficient process control. 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
17.32 Estimating the control chart limits from past data. Table 17.7 gives data on the losses (in dollars)incurred by a hospital in treating DRG 209 (major joint replacement) patients.10 The hospital has taken from its records a random sample of 8 such patients each month for 15 months.(a) Make an
17.31 Reevaluating the process parameters. The x and s control charts for the mesh-tensioning example(Figures 17.4 and 17.7) were based on μ = 275 mV and σ = 43 mV. Table 17.1 gives the 20 most recent samples from this process.(a) Estimate the process μ and σ based on these 20 samples.(b) Your
17.30 Altering the sampling plan. Refer to Exercise 17.29. Suppose instead that each sample contains an equal number of invoices from each clerk.(a) Sketch the x and s chart patterns that will result.(b) The process in this case will appear in control.When might this be an acceptable conclusion?
17.29 CHALLENGE Control chart for an unusual sampling situation. 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
17.28 More on updating control chart limits. In Exercise 17.13, control limits for the weight of ground beef were obtained using historical results. Using Table 17.3, estimate the process μ and process σ. Do either of these values suggest a change in the process center and spread?
17.27 Updating control chart limits. Suppose that when the process improvement project of Example 17.11 (page 17-25) is complete, the points remaining after removing special causes have x = 48.1 and s = 0.93. What are the center line and control limits for the x and s charts you would use to
17.26 The effect of special cause variation. Is each of the following examples of a special cause most likely to first result in (i) one-pointout 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
17.25 What’s wrong? For each of the following, explain what is wrong and why.(a) For the one-point-out rule, you could speed up the response to lack of control by using 4σ control limits.(b) In speeding up the response of a control chart to lack of control, we decrease the frequency of false
17.24 What’s wrong? For each of the following, explain what is wrong and why.(a) The R chart monitors the center of the process.(b) The R chart is commonly used because the range R is more informative than the standard deviation s.

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Introduction To The Practice Of Statistics 6th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions

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