The Practice Of Statistics For Business And Economics 4th Edition Layth C. Alwan, Bruce A. Craig - Solutions

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3.11 With reference to Figure 3.4, what events are represented by (a) region 5; (b) regions 4 and 6 together; (c) regions 7 and 8 together; (d) regions 1, 2, 3 and 5 together?
3.10 With reference to Exercise 3.9, what events are represented by (a) regions 1 and 3 together; (b) regions 3 and 4 together; (c) regions 1, 2, and 3 together?
3.9 In Figure 3.6,C is the event that an ore contains copper and U is the event that it contains uranium. Explain inwords what events are represented by regions 1, 2, 3, and 4. C 2 1 3 U S
3.8 For each of the following experiments, decide whether it would be appropriate to use a sample space which is finite, countably infinite, or continuous. (a) A Geiger counter, located adjacent to a building containing a reactor, will record the total number of alpha particles during a one-hour
3.7 Four supervisors and 3 engineers are responsible for work at a construction site, and at least 2 supervisors and one engineer have to be present at all times. (a) Using two coordinates so that (2, 1), for example, represents the event that 2 supervisors and one engineer are present, draw a
3.6 With reference to Exercise 3.5, which of the pairs of events, P and Q, Q and R, R and S, and P and S, are mutually exclusive?
3.5 To construct sample spaces for experiments in which we deal with non-numerical data, we often code the various alternatives by assigning them numbers. For instance, if an engineer is asked to rate the performance of a new machine with respect to its replacement as poor, not satisfactory, no
3.4 With reference to the sample space of Figure 3.1, express each of the following events in words. (a) F = {(1, 0), (1, 1)} (b) G = {(0, 2), (1, 1), (2, 0)} (c) F ∩ G
3.3 With reference to Exercise 3.1, list the outcomes comprising each of the following events, and also express the events in words. (a) A ∪ B (b) B ∩ C (c) B
3.2 With reference to Exercise 3.1, which of the three pairs of events, A and B, B and C, and B and C, are mutually exclusive?
3.1 A civil engineer suspects that the cement being supplied for constructing a dam is adulterated. There are three units of white cement and three units of black cement. He will check all six for adulteration. (a) Express each outcome using two coordinates, so (1, 2), for example, represents the
2.78 Given a stem-and-leaf display, is it possible to determine whether or not an outlier is present? Explain.
2.77 Given a five-number summary, minimum Q1 Q2 Q3 maximum is it possible to determine whether or not an outlier is present? Explain.
2.76 The National Highway Traffic Safety Administration reported the relative speed (rounded to the nearest 5 mph) of automobiles involved in accidents one year. The percentages at different speeds were 20 mph or less 2.0% 25 or 30 mph 29.7% 35 or 40 mph 30.4% 45 or 50 mph 16.5% 55 mph 19.2% 60 or
2.75 An engineer was assigned the task of calculating the average time spent by vehicles waiting at traffic signals. The signal timing (in seconds) would then be modified to reduce the pressure of traffic. The observations of average waiting time during the month of January are: 58 63 58 12 24 47
2.74 With reference to the lumber-strength data in Exercise 2.59, the statistical software package SAS produced the output in Figure 2.20. Using this output, (a) identify the mean and standard deviation and compare these answers with the values given in Exercise 2.59. (b) Create a boxplot. The
2.73 During the laying of gas pipelines, the depth of the pipeline (in mm) must be controlled. One service provider recorded depths of 418 428 431 420 412 425 423 433 417 420 410 431 429 425 (a) Find the sample mean. (b) Find the sample standard deviation. (c) Find the coefficient of variation. (d)
2.72 With reference to the aluminum-alloy strength data in Example 7, make a stem-and-leaf display.
2.71 With reference to Exercise 2.70, construct (a) a boxplot. (b) a modified boxplot.
2.70 The weight (grams) of meat in a pizza product produced by a large meat processor is measured for a sample of n = 20 packages. The ordered values are (Courtesy of Dave Brauch) 16.12 16.77 16.87 16.91 16.96 16.99 17.02 17.19 17.20 17.26 17.36 17.39 17.39 17.62 17.63 17.76 17.85 17.86 17.91
2.69 With reference to Exercise 2.68, (a) find the quartiles; (b) find the minimum, maximum, range, and interquartile range; (c) construct a boxplot.
2.68 An electric engineer monitored the flow of current in a circuit by measuring the flow of electrons and the resistance of the medium. Over 11 hours, she observed a flow of 5 12 8 16 13 10 9 11 14 7 8 amperes. (a) Create a dot diagram. (b) Find the median and the mean. Locate both on the dot
2.67 With reference to Exercise 2.66, (a) find the quartiles; (b) find the minimum, maximum, range, and interquartile range; (c) create a boxplot.
2.66 A. A. Michelson (1852–1931) made many series of measurements of the speed of light. Using a revolving mirror technique, he obtained 12 30 30 27 30 39 18 27 48 24 18 for the differences (velocity of light in air) − (229,700) km/s (Source: The Astrophysical Journal 65 (1927): 11.) (a) Create
2.65 With reference to Exercise 2.64, (a) calculate the median, maximum, minimum, and range for Tube 1 observations;(b) calculate the median, maximum, minimum, and range for the Tube 2 observations.
2.64 J. J. Thomson (1856–1940) discovered the electron by isolating negatively charged particles for which he could measure the mass/charge ratio. This ratio appeared to be constant over a wide range of experimental conditions and, consequently, could be a characteristic of a new particle. His
2.63 Direct evidence of Newton’s universal law of gravitation was provided from a renowned experiment by Henry Cavendish (1731–1810). In the experiment, masses of objects were determined by weighing, and the measured force of attraction was used to calculate the density of the earth. The
2.62 Create (a) a frequency table of the interrequest time data on page 29 using the intervals [0, 2,500), [2,500, 5,000), [5,000, 10,000), [10,000, 20,000), [20,000, 40,000), [40,000, 60,000), [60,000, 80,000), where the left-hand endpoint is included but the right-hand endpoint is not (b) a
2.61 Create (a) a frequency table of the aluminum alloy strength data on page 29 using the classes [66.0, 67.5), [67.5, 69.0), [69.0, 70.5), [70.5, 72.0), [72.0, 73.5), [73.5, 75.0), [75.0, 76.5), where the righthand endpoint is excluded (b) a histogram using the frequency table in part (a)
2.60 From 1,500 wall clocks inspected by a manufacturer, the following defects were recorded. hands touch each other 112 defective gears 16 faulty machinery 18 rotating pin 6 others 3 Create a Pareto chart.
2.59 (Further MINITAB calculation and graphs.) With the observations on the strength (in pounds per square inch) of 2 × 4 pieces of lumber already set in C1, the sequence of choices and clicks produces an even more complete summary (see Figure 2.17).The ordered strength data are 1325 1419 1490
2.58 Modern computer software programs have come a long way toward removing the tedium of calculating statistics. MINITAB is one common and easy-to-use program. We illustrate the use of the computer using MINITAB commands. Other easy-to-use programs have a quite similar command structure. The
2.57 The formula for the preceding exercise is a special case of the following formula for the weighted mean: xw = k i=1 wi xi k i=1 wi where wi is a weight indicating the relative importance of the ith observation. (a) If an instructor counts the final examination in a course four times as
2.56 If k sets of data consist, respectively, of n1, n2,..., nk observations and have the means x1, x2,..., xk, then the overall mean of all the data is given by the formula x = k i=1 ni xi k i=1 ni (a) There are 15 students in semester I, 25 students in semester II and 16 students in semester
2.55 To find the first and third quartiles Q1 and Q3 for grouped data, we proceed as in Exercise 2.53, but count n 4 and 3 n 4 of the observations instead of n 2 . (a) With reference to the distribution of the nanopillar height data on page 25 and the frequency distribution on page 26, find Q1,
2.54 For each of the following distributions, decide whether it is possible to find the mean and whether it is possible to find the median. Explain your answers. (a) Grade Frequency 40–49 5 50–59 18 60–69 27 70–79 15 80–89 6 (b) IQ Frequency less than 90 3 90–99 14 100–109 22
2.53 Median of grouped data To find the median of a distribution obtained for n observations, we first determine the class into which the median must fall. Then, if there are j values in this class and k values below it, the median is located (n/2) − k j of the way into this class, and to
2.52 If data are coded so that xi = c · ui +a, show that x = c · u + a and sx = | c | · su.
2.51 Show that the computing formula for s2 on page 44 is equivalent to the one used to define s2 on page 37.
2.48 Use the distribution obtained in Exercise 2.12 on page 33 to find the mean and the standard deviation of the particle sizes. Also determine the coefficient of variation. 2.49 Use the distribution obtained in Exercise 2.14 on page 33 to find the coefficient of variation of the temperature
2.46 Find the mean and the standard deviation of the 20 humidity readings on page 31 by using (a) the raw (ungrouped) data (b) the distribution obtained in that example 2.47 Use the distribution in Exercise 2.10 on page 32 to find the mean and the variance of the nanopillar diameters.
2.45 Refer to Exercise 2.44. The measurements for the 8 panels that did not fail were Good 33.5 32.25 34.75 34.25 35.5 33.0 36.25 35.75 (a) Calculate the sample mean x. (b) Calculate the sample standard deviation s. (c) Does there appear to be a major difference in board area between panels in
2.44 A factory experiencing a board-solder defect problem with an LED panel board product tested each board manufactured for LED failure. Data were collected on the area of the board on which LEDs were soldered for 8 bad panels and 8 good panels that passed the failure test. Failure 32.5 34.5 33.5
2.43 With reference to Exercise 2.14 on page 34, draw a boxplot.
2.42 For the five observations 8 2 10 6 9 (a) calculate the deviations ( xi − x ) and check that they add to 0. (b) calculate the variance and the standard deviation.
2.41 The Aerokopter AK1-3 is an ultra-lightweight manned kit helicopter with a high rotor tip speed. A sample of 8 measurements of speed, in meters per second, yielded 204 208 205 211 207 201 201 203 Find the mean and quartiles for this sample.
2.40 With reference to Exercise 2.31, find s2 using (a) the formula that defines s2; (b) the handheld calculator formula for s2.
2.39 Meat products are regularly monitored for freshness. A trained inspector selects a sample of the product and assigns an offensive smell score between 1 and 7 where 1 is very fresh. The resulting offensive smell scores, for each of 16 samples, are (Courtesy of David Brauch) 3.2 3.9 1.7 5.0 1.9
2.38 With reference to the preceding exercise, find s using (a) the formula that defines s; (b) the handheld calculator formula for s.
2.37 The output of an instrument is often a waveform. With the goal of developing a numerical measure of closeness, scientists asked 11 experts to look at two waveforms on the same graph and give a number between 0 and 1 to quantify how well the two waveforms agree.4 The agreement numbers for one
2.36 Records show that the normal daily precipitation for each month in the Gobi desert, Asia is 1, 1, 2, 4, 7, 15, 29, 27, 10, 3, 2 and 1 mm. Verify that the mean of these figures is 8.5 and comment on the claim that the average daily precipitation is a very comfortable 8.5 mm.
2.35 If the mean annual compensation paid to the chief executives of three engineering firms is $175,000, can one of them receive $550,000?
2.34 A contract for the maintenance of a leading manufacturer’s computers was given to a team of specialists. After six months, the supervisor of the team felt that computer performance could be improved by modifying the existing IC board. To document the current status, the team collected
2.33 Engineers3 are developing a miniaturized robotic capsule for exploration of a human gastrointestinal tract. One novel solution uses motor-driven legs. The engineers’ best design worked for a few trials, and then debris covered the tip of the leg and performance got worse. After cleaning,
2.32 At the end of 2012, nine skyscrapers in the world were over 300 meters tall. The ordered values of height are 366 381 442 452 484 492 508 601 828 The tallest is in Dubai. (a) Calculate the sample mean (b) Drop the largest value and re-calculate the mean. (c) Comment on effect of dropping the
2.31 Referring to Exercise 1.8 in Chapter 1, we see that the sample of 4 deviations (observation − specification) during the second hour for a critical crank-bore diameter is −6 1 −4 −3 ten-thousandths of an inch. For these 4 deviations (a) calculate the sample mean x (b) calculate the
2.30 Is the influence of a single outlier greater on the sample range or the interquartile range? Explain.
2.29 Is the influence of a single outlier greater on the mean or the median? Explain.
2.28 In each of the following situations, should your value be near the average or an outlier? If outlier, should it be too large or too small? (a) The time you take to complete a lab assignment next week (b) Your white blood cell count
2.27 In each of the following situations, should your value be near the average or an outlier? If an outlier, should it be too large or too small? (a) Income on your starting job (b) Your score on the final exam in a physics class (c) Your weight in 10 years
2.26 If the double-stem display has too few stems, we create 5 stems where the first holds leaves 0 and 1, the second holds 2 and 3, and so on. The resulting stem-and-leaf display is called a five-stem display. (a) The following are the IQs of 20 applicants to an undergraduate engineering program:
2.25 To construct a stem-and-leaf display with more stems than there would be otherwise, we might repeat each stem. The leaves 0, 1, 2, 3, and 4 would be attached to the first stem and leaves 5, 6, 7, 8, and 9 to the second. For the humidity readings on page 31, we would thus get the double-stem
2.24 List the data that correspond to the following stems of stem-and-leaf displays: (a) 4 | 0 1 1 2 5 7 Leaf unit = 1.0 (b) 62 | 3 5 5 8 9 Leaf unit = 1.0 (c) 8 | 01 23 62 91 First leaf digit unit = 10.0 (d) 2.28 | 4 5 6 6 8 9 Leaf unit = 0.001
2.23 The following are determinations of a river’s annual maximum flow in cubic meters per second: 405, 355, 419, 267, 370, 391, 612, 383, 434, 462, 288, 317, 540, 295, and 508. Construct a stem-and-leaf display with two-digit leaves.
2.22 The following are figures on sacks of cement used daily at a construction site: 75, 77, 82, 45, 55, 90, 80, 81, 76, 47, 59, 52, 71, 83, 91, 76, 57, 59, 43 and 79. Construct a stem-and-leaf display with the stem labels 4, 5, ... , and 9.
2.21 Convert the distribution of nanopillar heights on page 26 into a distribution having the classes (205, 245], (245, 325], (325, 365], (365, 405], where the right-hand endpoint is included. Draw two histograms of this distribution, one in which the class frequencies are given by the heights of
2.20 Categorical distributions are often presented graphically by means of pie charts, in which a circle is divided into sectors proportional in size to the frequencies (or percentages) with which the data are distributed among the categories. Draw a pie chart to represent the following data,
2.19 The pictogram of Figure 2.11 is intended to illustrate the fact that per capita income in the United States doubled from $21,385 in 1993 to $42,643 in 2012. Does this pictogram convey a fair impression of the actual change? If not, state how it might be modified. $21,385 $42,643 1993 2012
2.18 Referring to Exercise 2.17, graph the empirical cumulative distribution for the data in Exercise 2.16.
2.17 Given a set of observations x1, x2,... , xn, we define their empirical cumulative distribution as the function whose values F(x) equals the proportion of the observations less than or equal to x. Graph the empirical cumulative distribution for the 15 measurements of Exercise 2.3.
2.16 The following are the number of transistors failing a quality check per hour during 72 observed hours of production: 246812185461 018234125118 219142568171 491824118553 091971887772 712735885990 Group these data into a frequency distribution showing how often each of the values occurs and
2.15 Convert the distribution obtained in Exercise 2.14 into a cumulative “less than” distribution and plot its ogive.
2.14 An engineer uses a thermocouple to monitor the temperature of a stable reaction. The ordered values of 50 observations (Courtesy of Scott Sanders), in tenths of ◦C, are 1.11 1.21 1.21 1.21 1.23 1.24 1.25 1.25 1.27 1.27 1.28 1.29 1.31 1.31 1.31 1.32 1.34 1.34 1.35 1.36 1.36 1.36 1.36 1.36
2.13 Convert the distribution obtained in Exercise 2.12 into a cumulative “less than” distribution and plot its ogive.
2.12 The following are the sizes of particles of cement dust (given to the nearest hundredth of a micron) in a cement factory: 16.12 10.48 11.12 16.18 18.13 19.10 13.21 10.12 21.18 15.12 10.11 13.31 18.61 11.43 18.26 13.77 13.24 12.16 17.19 11.36 12.53 13.25 10.67 15.45 14.28 14.32 15.18 14.21
2.11 Convert the distribution obtained in the preceding exercise into a cumulative “less than or equal to” distribution and graph its ogive.
2.10 To continually increase the speed of computers, electrical engineers are working on ever-decreasing scales.The size of devices currently undergoing development is measured in nanometers (nm), or 10−9× meters. Engineers fabricating a new transmission-type electron multiplier2 created an
2.9 With reference to the preceding exercise, is it possible to determine from the grouped data how many turbo pumps have a power generation of (a) more than 50.0? (b) less than 50.0? (c) at most 60.0? (d) at least 60.0? (e) 50.0 to 60.0 inclusive?
2.8 The power generated (MW) by liquid hydrogen turbo pumps, given to the nearest tenth, is grouped into a table having the classes [40.0, 45.0), [45.0, 50.0), [50.0, 55.0), [55.0, 60.0) and [60.0, 65.0), where the left-hand endpoint is included but the right-hand endpoint is not. Find (a) the
2.7 Physicists first observed neutrinos from a supernova that occurred outside of our solar system when the detector near Kamiokande, Japan, recorded twelve arrivals. The times(seconds) between the neutrinos are 0.107 0.196 0.021 0.281 0.179 0.854 0.58 0.19 7.30 1.18 2.00 (a) Draw a dot diagram.
2.6 A dam on a river holds water in its reservoir to generate electricity. Because the dam is in a rainforest area, the flow of water is highly uncertain. In December last year, the overflow from the reservoir (in million cubic meters) on 14 different days was 26 24 25.5 23.5 25.5 23 23 24 25 24
2.5 Civil engineers help municipal wastewater treatment plants operate more efficiently by collecting data on the quality of the effluent. On seven occasions, the amounts of suspended solids (parts per million) at one plant were 14 12 21 28 30 65 26 Display the data in a dot diagram. Comment on
2.4 To determine the strengths of various detergents, the following are 20 measurements of the total dissolved salts (parts per million) in water: 168 170 148 160 168 164 175 178 165 168 152 170 172 192 182 164 152 160 170 172 Construct a dot diagram.
2.3 Tests were conducted to measure the running temperature for engines (in °F). A sample of 15 tests yielded the temperature values: 182 184 184 186 180 198 195 194 197 200 188 188 194 197 184 Construct a dot diagram.
2.2 Losses at an oil refinery (in millions of dollars) due to excess heat can be divided according to the reason behind the generation of excessive heat. oversupplying fuel 202 excess air 124 carelessness of operator 96 incomplete combustion 27 (a) Draw a Pareto chart. (b) What percent of the loss
2.1 Damages at a factory manufacturing chairs are categorized according to the material wasted. plastic 75 iron 31 cloth 22 spares 8 Draw a Pareto chart.
1.8 A Canadian manufacturer identified a critical diameter on a crank bore that needed to be maintained within a close tolerance for the product to be successful. Samples of size 4 were taken every hour. The values of the differences (measurement − specification), in tenthousandths of an inch,
1.7 Refer to the slot depth data in Table 1.1. After the machine was repaired, a sample of three new ceramic parts had slot depths 215, 216, and 213 (thousandths of an inch). (a) Redraw the X-bar chart and include the additional mean x. (b) Does the new x fall within the control limits?
1.6 Ten seniors have applied to be on the team that will build a high-mileage car to compete against teams from other universities. Use Table 7 of random digits to select 5 of the 10 seniors to form the team.
1.5 For ceiling fans to rotate effectively, the bending angle of the individual paddles of the fan must remain between tight limits. From each hour’s production, 25 fans are selected and the angle is measured. Identify the population unit, variable of interest, statistical population, and sample.
1.4 Identify the statistical population, sample, and variable of interest in each of the following situations: (a) Tensile strength is measured on 20 specimens of super strength thread made of the same nanofibers. The intent is to learn about the strengths for all specimens that could conceivably
1.3 Consider the population of all cars owned by women in your neighborhood. You want to know the model of the car. (a) Specify the population unit. (b) Specify the variable of interest. (c) Specify the statistical population.
1.2 A television channel announced a vote for their viewers’ favorite television show. Viewers were asked to visit the channel’s website and vote online for their favorite show. Identify the population in terms of preferences, and the sample. Is the sample likely to be representative?
1.1 An article in a civil engineering magazine asks “How Strong Are the Pillars of Our Overhead Bridges?” and goes on to say that samples were collected of materials being used in the construction of 294 overhead bridges across the country. Let the variable of interest be a numerical measure
Daily trading volume of FedEx. Refer to Example 13.22 (page 686) in which a prediction of logged trading volume of FedEx stock for period 150 was made.(a) Exponentiate the log prediction value back to original units. What is the interpretation of the estimate?(b) Refer now to Example 13.18 (pages
Monthly warehouse club and superstore sales. Consider the monthly warehouse club and superstore sales series discussed in Examples 13.15 and 13.16 (pages 671–674). CLUB(a) Use the moving-average approach to compute seasonal ratios and report their values.(b) Produce and plot the seasonally
U.S. air carrier traffic. Consider monthly total number of passenger miles on U.S. domestic flights from the previous exercise. AIRTRAV(a) Use the moving-average approach to compute seasonal ratios and report their values.(b) Produce and plot the seasonally adjusted series. What are your
U.S. air carrier traffic. How much more or less are Americans taking to the air? Consider a time series of monthly total number of passenger miles (in thousands)on U.S. domestic flights starting with January 2009 and ending with May 2014.40 AIRTRAV(a) Make a time plot of monthly miles. Describe the
Exponential smoothing for unemployment rate. Consider the annual unemployment rate time series from Exercise 13.38 (page 690). UNEMPL(a) Use statistical software to determine the optimal smoothing constant w. Does this optimal w fall in the traditional range for w? Explain.(b) The series ended with
U.S. poverty rate, continued. Continue the analysis of the annual U.S. poverty rate. POVERTY(a) Produce a PACF for the series. If a lag only based model were to be fit, how many lags does the PACF suggest?(b) Based on the PACF from part (a), fit a lag only based model. Report the estimated

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The Practice Of Statistics For Business And Economics 4th Edition Layth C. Alwan, Bruce A. Craig - Solutions

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