Questions and Answers of Applied Statistics and Probability

Unequal Sample Sizes. One application of the standardized control chart introduced in Exercise 15-140 is to allow unequal sample sizes on the control chart. Provide details concerning how this
Standardized Control Chart. Consider the P chart with the usual 3-sigma control limits. Suppose that we define a new variableas the quantity to plot on a control chart. It is proposed that this new
C Control Chart. An alternative to the U chart is a chart based on the number of defects. The chart has center line at nu, and the control limits are(a) Verify that the control limits provided are
NP Control Chart. An alternative to the control chart for fraction defective is a control chart based on the number of defectives or the NP control chart. The chart has center line at np̅, the
Consider a process whose specifications on a quality characteristic are 100 ± 15. You know that the standard deviation of this normally distributed quality characteristic is 5. Where should you
A process is controlled by a P chart using samples of size 100. The center line on the chart is 0.05. What is the probability that the control chart detects a shift to 0.08 on the first sample
Consider a random-effects model for the singlefactor completely randomized design. (a) Show that a 100(1 − α)% confidence interval on the ratio σ2τ / σ2 + σ2τ) iswhere L and U are as defined
Consider the random-effects model for the singlefactor completely randomized design. Show that a 100(1 − α)% confidence interval on the ratio of variance components σ2τ /σ2 is given byWhereAnd
Consider the random-effects model for the singlefactor completely randomized design. Show that a 100(1 − α)% confidence interval on the ratio of variance components σ2τ /σ2 is given byWhereAnd
Show that the variance of the linear combination
An article in Journal of Hazardous Materials [“Toxicity Assessment from Electro-Coagulation Treated-Textile Dye Waste Waters by Bioassays,” 2009, Vol. 172(1), pp. 330–337] discussed a study of
An article in Fuel Processing Technology (“Application of the Factorial Design of Experiments to Biodiesel Production from Lard,” 2009, Vol. 90, pp. 1447–1451) described an experiment to
Consider the following computer output for an experiment.(a) How many replicates did the experimenter use?(b) Fill in the missing information in the ANOVA table. Use bounds for the P-value.(c) What
Table E12-12 presents statistics for the NationalHockey League teams from the 2008–2009 season (TheSports Network). Fit a multiple linear regression modelthat relates wins to the variables GF
Consider the following computer output.(a) Fill in the missing values. Use bounds for the P-values.(b) Is the overall model significant at α = 0.05? Is it significant at α = 0.01?(c) Discuss the
Consider the following computer output.(a) Fill in the missing quantities. You may use bounds for the P-values.(b) What conclusions can you draw about the significance of regression?(c) What
Recall the regression of percent of body fat on heightand waist from Exercise 12-1. The simple regression model ofpercent of body fat on height alone shows the following:(a) Test whether the
Table E12-12 presents statistics for the NationalHockey League teams from the 2008–2009 season (TheSports Network). Fit a multiple linear regression modelthat relates wins to the variables GF
Table E12-11 presents quarterback ratings for the 2008 National Football League season (The Sports Network).(a) Fit a multiple regression model to relate the quarterbackrating to the percentage of
An article in Electronic Packaging and Production(2002, Vol. 42) considered the effect of X-ray inspection ofintegrated circuits. The rads (radiation dose) were studied as afunction of current (in
Can the percentage of the workforce who are engineersin each U.S. state be predicted by the amount of money spentin on higher education (as a percent of gross domestic product),on venture capital
A class of 63 students has two hourly exams and afinal exam. How well do the two hourly exams predict performance on the final?The following are some quantities of interest:(a) Calculate the least
Exercise 11.1 described a regression model betweenpercent of body fat (%BF) as measured by immersion and BMIfrom a study on 250 male subjects. The researchers also measured13 physical characteristics
Consider the following data. Suppose that the relation -ship between Y and x is hypothesized to be Y = (β0 + β1x + e)− . 1Fit an appropriate model to the data. Does the assumed modelform seem
An article in the IEEE Transactions on Instrumentationand Measurement [“Direct, Fast, and Accurate Measurementof VT and K of MOS Transistor Using VT-Sift Circuit”(1991, Vol. 40, pp. 951–955)]
The World Health Organization defines obesity inadults as having a body mass index (BMI) higher than 30. Of the250 men in the study mentioned in Exercise 11-1, 23 are by thisdefinition obese. How
The market research department of a soft drinkmanufacturer is investigating the effectiveness of a price discountcoupon on the purchase of a two-liter beverage product.A sample of 5500 customers was
The monthly absolute estimate of global (land andocean combined) temperature indexes (degrees C) in 2000 and2001 (www.ncdc.noaa.gov/oa/climate/) are:(a) Graph the data and fit a regression line to
Consider the following computer output.The regression equation isAnalysis of Variance(a) Fill in the missing information. You may use bounds for the P-values.(b) Can you conclude that the model
An article in the Journal of the Environmental Engineering Division [“Least Squares Estimates of BOD Parameters” (1980, Vol. 106, pp. 1197–1202)] took a sample from the Holston River below
An article in the Journal of the AmericanCeramic Society [“Rapid Hot-Pressing of Ultrafi ne PSZPowders” (1991, Vol. 74, pp. 1547–1553)] considered themicrostructure of the ultrafi ne powder of
On average, do people gain weight as they age? Usingdata from the same study as in Exercise 11-1, we provide somesummary statistics for both age and weight.(a) Calculate the least squares estimates
A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers who are familiar with both languages are asked to code
Consider the following computer output.Difference = mu (1) – mu (2)Estimate for difference: –1.21095% CI for difference: (–2.560, 0.140)T-test of difference = 0 (vs not =) :T-value = ? P-value
Output from a software package follows:(a) Fill in the missing items. What conclusions would you draw?(b) Is this a one-sided or a two-sided test?(c) Use the normal table and the preceding data to
X̅1 and S21 are the sample mean and sample variancefrom a population with mean μ1 and variance σ12. Similarly,X̅2 and S22 are the sample mean and sample variance from asecond independent
The rate of return of an asset is the change in price dividedby the initial price (denoted as r ). Suppose that $10,000 is usedto purchase shares in three stocks with rates of returns X1,X2
In the transmission of digital information, the probability that a bit has high, moderate, or low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that
Zeitler€™s Department Stores sells its products online and through traditional brick-andmortar stores. The following parallel-coordinates plot displays data from a sample of 20 customers
During each month, there is enough production capacity to produce up to 32,000 total balls (football 1 soccer balls), and there is enough storage capacity to store up to 20,000 total balls (football
A European put option on a currency allows you to sell a unit of that currency at the specified strike price (exchange rate) at a particular point in time after the purchase of the option. For
As admissions director for an exclusive executive MBA program which takes place on Necker Island in the Caribbean, Richard Branson must decide which applicants should receive admission offers. This
Bianca Peterson is a marketing engineer for Hexagon Composites, a company which sells carbon composite storage tanks. In an effort to gain product adoptions from customers, Bianca goes on sales trips
Young entrepreneur Fan Bingbing has launched a business venture in which she uses stories submitted by university students as the basis for comics in a monthly animestyle magazine. Based on market
Steve Austin is the fleet manager for SharePlane, a company that sells fractional ownership of private jets. SharePlane must carefully maintain their jets at all times. If a jet breaks down, it must
You are considering the purchase of a new car and are weighing the choice between a Ford Fusion Hybrid sedan (which assists a gasoline engine with an electric motor powered via regenerative braking)
Using the file LandSharkBeta, evaluate bid amounts from $1,229,000 to $1,329,000 in increments of $20,000 by building a table listing 95% confidence intervals around the average return and
The Dallas Mavericks and the Golden State Warriors are two teams in the National Basketball Association. Dallas and Golden State will play multiple times over the course of an NBA season. Assume that
Goal Kick Sports (GKS) is a retail chain that sells youth and adult soccer equipment. The GKS financial planning group has developed a spreadsheet model to calculate the net discounted cash flow of
A well-respected polling agency has conducted a poll for an upcoming Presidential election. The polling agency has taken measures so that its random sample consists of 50,000 people and is
A random variable has a triangular probability density function with a = 50, b = 375, and m = 250.a. Sketch the probability distribution function for this random variable. Label the points a = 50, b
The online review service Yelp helps millions of consumers find the goods and services they seek. To help consumers make more-informed choices, Yelp includes over 120 million reviews. The file
Companies can learn a lot about customer experiences by monitoring the social media web site Twitter. The file AirlineTweets contains a sample of 36 tweets of an airline’s customers. Normalize the
Josephine Mater works for the supply-chain analytics division of Trader Joe’s, a national chain of specialty grocery stores. Trader Joe’s is considering a redesign of its supply chain. Josephine
Apply k-means clustering with values of k = 2, 3, 4, and 5 to cluster the data in DemoKTC based on the Age, Income, and Children variables. Normalize the values of the input variables to adjust for
Leggere, an internet book retailer, is interested in better understanding the purchase decisions of its customers. For a set of 2,000 customer transactions, it has categorized the individual book
Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table.Jay has
Amanda Boleyn, an entrepreneur who recently sold her start-up for a multi-million-dollar sum, is looking for alternate investments for her newfound fortune. She is considering an investment in wine,
In an effort to inform political leaders and economists discussing the deregulation of electric and gas utilities, data on eight numerical variables from utility companies have been grouped using
The regulation of electric and gas utilities is an important public policy question affecting consumer€™s choice and cost of energy provider. To inform deliberation on public policy, data
For this problem we will use the data in the file Global100 that was referenced in Section 3.4 as an example for creating a treemap. Here we will use these data to create a GIS chart. A portion of
Approximately 1.65 million high school students take the Scholastic Aptitude Test (SAT) each year, and nearly 80% of the college and universities without open admissions policies use SAT scores in
Huron Lakes Candies (HLC) has developed a new candy bar called Java Cup that is a milk chocolate cup with a coffee-cream center. In order to assess the market potential of Java Cup, HLC has developed
Marilyn Marshall, a Professor of sports economics, has obtained a data set of home attendance for each of the 30 major league baseball franchises for each season from 2010 through 2016. Dr. Marshall
The following table shows an example of gross domestic product values for five countries over six years in equivalent U.S. dollars ($).a. How could you improve the readability of this table?b. The
Below is a sample of the data in the file NFLAttendance which contains the 32 teams in the National Football League, their conference affiliation, their division, and their average home attendance.a.
Analyze the develop or contract decision problem in Example 15-9 based on the best-case (optimistic) criterion and determine the actions selected at each decision node. Do any actions differ from
Reconsider the extended warranty decision in Example 15-8. Determine the cost of the extended warranty so that the expected costs of the actions to either purchase the warranty or not are
Suppose that a P chart with center line at p̅ and k-sigma control limits is used to control a process. What is the smallest sample size that can be used on this control chart to ensure that the
Suppose that a P chart with center line at p with k-sigma control limits is used to control a process. There is a critical fraction defective pc that must be detected with probability 0.50 on the
Suppose that an X̅ chart is used to control a normally distributed process and that samples of size n are taken every n hours and plotted on the chart, which has k-sigma limits.(a) Find a general
Consider an X̅ control chart with k-sigma control limits and subgroup size n. Develop a general expression for the probability that a point plots outside the control limits when the process mean has
Suppose that a process is in control, and 3-sigma control limits are in use on an X̅ chart. The subgroup size is 4. Let the mean shift by 1.5σ. What is the probability that this shift remains
Consider the infectious-waste data in Exercise 15-26. Use the data after the process change only.(a) Construct an CUSUM control chart with the target equal to the estimated process mean, k = 0.5, and
An article in Electric Power Systems Research [€œOn the Self-Scheduling of a Power Producer in Uncertain Trading Environments€ (2008) considered a self-scheduling approach for a
Consider the TAT data in Exercise 15-18.(a) Construct an CUSUM control chart with the target equal to the estimated process mean, k = 0.5, and h = 4. Does the process appear to be in control at the
A process is controlled by a P chart using samples of size 100. The center line on the chart is 0.05.(a) What is the probability that the control chart detects a shift to 0.08 on the first sample
Analyze Example 15-9 based on the expected profit criterion and determine the actions that are selected at each decision node. Do any actions differ from those selected in the example?Example 15-9In
Analyze Example 15-9 based on the most probable criterion and determine the actions that are selected at each decision node. Do any actions differ from those selected in the example?Example 15-9In
Reconsider the extended warranty decision in Example 15-8. Suppose that the probabilities of the major, minor, and no repair states are changed to 0.2, 0.4, and 0.4, respectively. Determine the
Suppose that the cost of a major repair without the extended warranty in Example 15-8 is changed to $1000. Determine the decision selected based on the minimax, most probable, and expected cost
Consider an EMWA control chart. The target value for the process is Î¼0= 50 and Ïƒ = 2. Use Table 15-11.(a) If the sample size is n = 1, would you prefer an EWMA chart with
Consider the concentration data in Exercise 15-76. Use σ = 8 and assume that the desired process target is 100.(a) Construct an EWMA control chart with λ = 0.2. Does the process appear to be in
Consider the diameter data in Exercise 15-75. Assume that the desired process target is 10.0 millimeters.(a) Estimate the process standard deviation.(b) Construct an EWMA control chart with
Consider the purity data in Exercise 15-74. Use Ïƒ = 0.8 and assume that the desired process target is 90. (a) Construct an EWMA control chart with Î» = 0.2. Does the
Consider a CUSUM with h = 5 and k = 1 / 2. Samples are taken every two hours from the process. The target value for the process is Î¼0= 50 and Ïƒ = 2. Use Table 15-10.Table
The concentration of a chemical product is measured by taking four samples from each batch of material. The average concentration of these measurements for the last 20 batches is shown in the
An automatic senson measures the diameter of holes in consecutive order. The results of measuring 25 holes follow.(a) Estimate the process standard deviation.(b) Set up a CUSUM control procedure,
The purity of a chemical product is measured every two hours. The results of 20 consecutive measurements are as follows:(a) Set up a CUSUM control chart for this process. Use Ïƒ = 0.8 in
The following data were considered in Quality Engineering [€œParabolic Control Limits for The Exponentially Weighted Moving Average Control Charts in Quality Engineering€ (1992,
Consider the U chart for printed circuit boards in Example 15-5. The center line = 1.6, UCL = 3.3, and n = 5.(a) Calculate the LCL and UCL.(b) Suppose that the true mean defects per unit shifts from
Consider a P-chart with subgroup size n = 50 and center line at 0.12.(a) Calculate the LCL and UCL.(b) Suppose that the true proportion defective changes from 0.12 to 0.18. What is the ARL after the
Consider an X̅ control chart with UCL = 24.802, LCL = 23.792, and n = 3. Suppose that the mean shifts to 24.2.(a) What is the probability that this shift is detected on the next sample?(b) What is
An X̅ chart uses a sample of size 3. The center line is at 200, and the upper and lower 3-sigma control limits are at 212 and 188, respectively.(a) Estimate the process σ.(b) Suppose that the
Consider the revised XÌ… control chart in Exercise 15-8 with ÏƒÌ‚ = 0.669, UCL = 7.443, LCL = 5.125, and n = 3. Suppose that the mean shifts to 5.5.(a) What is the
Consider an X̅ control chart with r̅ = 0.000924, UCL = 0.0635, LCL = 0.0624, and n = 5. Suppose that the mean shifts to 0.0625.(a) What is the probability that this shift is detected on the next
Consider an X̅ control chart with r̅ = 2.25, UCL = 17.40, LCL = 12.79, and n = 3. Suppose that the mean shifts to 13.(a) What is the probability that this shift is detected on the next sample?(b)
Consider an X̅ control chart with σ̂ = 2.466, UCL = 37.404, LCL = 30.780, and n = 5. Suppose that the mean shifts to 36.(a) What is the probability that this shift is detected on the next
Consider an X̅ control chart with σ̂ = 1.40, UCL = 21.71, LCL = 18.29, and n = 6. Suppose that the mean shifts to 17.(a) What is the probability that this shift is detected on the next sample?(b)
Consider an X̅ control chart with r̅ = 34.286, UCL = 242.780, LCL = 203.220, and n = 5. Suppose that the mean shifts to 210.(a) What is the probability that this shift is detected on the next

Showing 1 - 100 of 1158