Applied Statistics And Probability For Engineers 5th Edition Douglas C. Montgomery, George C. Runger - Solutions

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Write the results for Problem 8.2 so they would be suitable for inclusion in a report. Include table(s) that present the results the reader should see.
Fit the regression plane for the fathers using FFVC as the dependent variable and age and height as the independent variables.
Using the chemical companies’ data in Table 9.1, predict the price earnings (P/E) ratio from the debt to equity (D/E) ratio, the annual dividends divided by the 12-months’ earnings per share (PAYOUTR1), and the percentage net profit margin (NPM1).Obtain the correlation matrix, and check the
Using the summary variable describing the neighborhood in Problem 7.15, generate a loess graph to examine the relationship between this variable and the age at which adolescents started using marijuana. Interpret the graph.
For the Parental HIV data generate a variable that represents the sum of the variables describing the neighborhood where the adolescent lives (NGHB1–NGHB11). Does the age at which adolescents start smoking depend on the score describing the neighborhood?
For the Parental HIV data produce a scatterplot of the age at which adolescents first started smoking versus the age at which they first started drinking alcohol. Based on the graph, do adolescents tend to start smoking before drinking alcohol, or vice versa? Calculate the correlation coefficient.
For the mother, perform a regression of FEV1 on weight. Test whether the coefficients are zero. Plot the regression line on a scatter diagram of MFEV1 versus MWE1. On this plot, identify the following groups of points:group 1: ID = 12, 33, 45, 42, 94, 144;group 2: ID = 7, 94, 105, 107, 115, 141,
Examine the residual plot from the regression of FEV1 on height for the oldest child. Choose an appropriate transformation, perform the regression with the transformed variable, and compare the results (statistics, plots) with the original regression analysis.
What is the correlation between height and weight in the oldest child? How would your answer to the last part of Problem 7.10 change if r = 1? r = ????1? r = 0?
For the oldest child, perform the following regression analyses: FEV1 on weight, FEV1 on height, FVC on weight, and FVC on height. Note the values of the slope and correlation coefficient for each regression and test whether they are equal to zero. Discuss whether height or weight is more strongly
From the depression data set described in Table 3.4 create a data set containing only the variables AGE and INCOME.a) Find the regression of income on age.b) Successively add and then delete each of the following points:AGE INCOME 42 120 80 150 180 15 and repeat the regression each time with the
(Continuation of Problem 7.7.) Calculate the variance of CESD for observations in each of the groups defined by income as follows: INCOME 59. For each observation, define a variable WEIGHT equal to 1 divided by the variance of a CESD within the income group to which it belongs. Obtain a weighted
Using the depression data set (see Table 3.4), perform a regression analysis of depression, as measured by CESD, on income. Plot the residuals. Does the normality assumption appear to be met? Repeat using the logarithm of CESD instead of CESD. Is the fit improved?
Examine the plot you produced in Problem 7.1 and choose some transformation for X and/or Y and repeat the analysis described there. Compare the correlation coefficients for the original and transformed variables, and decide whether the transformation helped. If so, which transformation was helpful?
Repeat Problem 7.2 using log(weight) and log(height) in place of the original variables. Using graphical and numerical devices, decide if the transformations help.
For the data in Problem 7.3, pretend that the index increases linearly in time and use linear regression to obtain an equation to forecast the index value as a function of time. Using “volume”as a weight variable, obtain a weighted least squares forecasting equation. Does weighted least squares
In Problem 5.8, the New York Stock Exchange Composite Index and daily volume for August 9 through September 17, 1982, were presented. Describe how volume appears to be affected by the price index, using regression analysis. Describe whether or not the residuals from your regression analysis are
From the family lung function data set in Appendix A, perform a regression analysis of weight on height for fathers. Repeat for mothers. Determine the correlation coefficient and the regression equation for fathers and mothers. Test that the coefficients are significantly different from zero for
In Table 9.1, financial performance data of 30 chemical companies are presented. Use growth in earnings per share, labelled EPS5, as the dependent variable and growth in sales, labelled SALESGR5, as the independent variable. (A description of these variables is given in Section 9.3.) Plot the data,
The Parental HIV data include information on the age at which adolescents started smoking.Where does this variable fit into Stevens’s classification scheme? Particularly comment on the issue relating to adolescents who had not starting smoking by the time they were interviewed.
Suppose you would like to analyze the relationship between the number of times an adolescent has been absent from school without a reason and how much the adolescent likes/liked going to school for the Parental HIV data (Appendix A). Suggest ways to analyze this relationship.Suggest other variables
In the depression study, information was obtained on the respondent’s religion (Chapter 3).Describe why you think it is incorrect to obtain an average score for religion across the 294 respondents.
Using the lung function data described in the Appendix, an investigator would like to predict a child’s lung function based on that of the parents and the area they live in. What analyses would be appropriate to use?
A psychologist would like to predict whether or not a respondent in the depression study described in Chapter 3 is depressed. To do this, she would like to use the information contained in the following variables: MARITAL, INCOME, and AGE. Suggest analyses.
Two methods are currently used to treat a particular type of cancer. It is suspected that one of the treatments is twice as effective as the other in prolonging survival regardless of the severity of the disease at diagnosis. A study is carried out. After the data are collected, what analysis
A member of the admissions committee notices that there are several women with high grade point averages but low SAT scores. He wonders if this pattern holds for both men and women in general, only for women in general, or only in a few cases. Suggest ways to analyze this problem.
For the data described in Problem 6.6 we wish to relate health data such as infant mortality(the proportion of children dying before the age of one year) and life expectancy (the expected age at death of a person born today if the death rates remain unchanged) to other data such as gross national
For the data described in the prior problem we wish to put together similar countries into groups. Suggest possible analyses.
Large amounts of data are available from the United Nations and other international organizations such as the World Bank for each country and sovereign state of the world, including health, education, and commercial data. An economist would like to invent a descriptive system for the degree of
Data on men and women who have died have been obtained from health maintenance organization records. These data include age at death, height and weight, and several physiological and lifestyle measurements such as blood pressure, smoking status, dietary intake, and usual amount of exercise. The
A college admissions committee wishes to predict which prospective students will successfully graduate. To do so, the committee intends to obtain the college grade point averages for a sample of college seniors and compare these with their high school grade point averages and Scholastic Aptitude
A coach has made numerous measurements on successful basketball players, such as height, weight, and strength. He also knows which position each player is successful at. He would like to obtain a function from these data that would predict which position a new player would be best at. Suggest an
An investigator is attempting to determine the health effects on families of living in crowded urban apartments. Several characteristics of the apartment have been measured, including square feet of living area per person, cleanliness, and age of the apartment. Several illness characteristics for
Compute an appropriate measure of the center of the distribution for the following variables from the depression data set: MARITAL, INCOME, AGE, and HEALTH.
Using the lung cancer data described in Appendix A, examine the distribution of the variable days separately for those who died (death=1) and for those who did not (death=0). Plot a normal probability plot, a histogram, and a boxplot for each. Use the methods described in this chapter to choose
Using the Parental HIV data calculate an overall Brief Symptom Inventory (BSI) score for each adolescent (see the codebook for details). Log-transform the BSI score. Obtain a normal probability plot for the log-transformed variables. Does the log-transformed variable seem to be normally
Using the Parental HIV data set (see Appendix A), plot a histogram, a boxplot, and a normal probability plot for the variable AGESMOKE. This variable is the age in years when the respondent started smoking. If the respondent did not start smoking, AGESMOKE was assigned a value of zero. Decide what
Repeat Problem 5.7 with weights expressed in ounces instead of pounds. How will your conclusions change? Obtain normal probability plots of the logarithm of mothers’ weights expressed in pounds and then in ounces, and compare.
Obtain a normal probability plot of the index given in Problem 5.8. Suppose that you had been ignorant of the lack of independence of these data and had treated them as if they were independent samples. Assess whether they are normally distributed.
Generate ten random normal deviates. Display a probability plot of these data. Suppose you didn’t know the origin of these data. Would you conclude they were normally distributed?What is your conclusion based on the Shapiro–Wilk test? Do ten observations provide sufficient information to check
The accompanying data are from the New York Stock Exchange Composite Index for the period August 9 through September 17, 1982. Run a program to plot these data in order to assess the lack of independence of successive observations. (Note that the data cover five days per week, except for a holiday
Obtain normal probability plots of mothers’ and fathers’ weights from the lung function data set described in Appendix A. Discuss whether or not you consider weight to be normally distributed in the population from which this sample is taken.
Take the logarithm of the CESD score plus 1 and compare the histograms of CESD and log(CESD + 1). (A small constant must be added to CESD because CESD can be zero.)
Use the two sets of 100 random numbers from Problem 5.4. Display boxplots of these two sets of values and state which of the three graphical methods (histograms, normal probability plots, and boxplots) are most useful in assessing normality.
Generate a set of 100 random normal deviates by using the random number generator in your software program of choice (R: rnorm, SAS: NORMAL, Stata: rnormal, SPSS:RV.NORMAL). Display a histogram and normal probability plot of these values. Square these numbers by using transformations. Compare
Repeat Problems 5.1 and 5.2, taking the square root of income.
Take the logarithm to base 10 of the income variable in the depression data set. Compare the histogram of income with the histogram of log(INCOME). Also, compare the normal probability plots of income and log(INCOME).
Using the depression data set described in Tables 3.4 and 3.5, create a variable equal to the negative of one divided by the cubic root of income. Display a normal probability plot of the new variable.
Using the mice data, create a profile plot for the average weight of mice per group over time.
Using a scatterplot matrix, repeat the Problem 4.8 for fathers’ measurements instead of those of the oldest child. Did you find the same pattern of relationships between body measurements and FEV1 in fathers as you did for the oldest child?
Using the parental HIV data set create a few visualizations to explore the relationship between the variables of interest listed below. In a few sentences describe the information about the given relationship you learn from each graph, and what specific features of the graph led you to that
Using the lung function data explore and describe the following relationships:a) How does the residential area affect the lung function of the parents?b) For the oldest child, plot the relationship between FEV1 and (i) age; (ii) height; (iii) weight using a scatterplot and lowess line.
Construct a scatterplot of income versus employment status from the depression data set. From the data in this table, decide if there are any adults whose incomes are unusual considering their employment status. Are there any adults in the data set whom you think are unusual?
For the lung cancer data set,a) produce a separate histogram of the variable Days for small and large tumor sizes (0 and 1 values of the variable Staget)b) compute a two-way frequency table of the variable Staget versus the variable Deathc) comment on the results of (a) and (b).
For the lung function data set, produce a two-way table of gender of child 1 versus gender of child 2 (for families with at least two children). Describe the distribution of genders for these families.
For the lung cancer data set,a) construct a histogram of the variable Daysb) for every other variable produce a frequency table of all possible values.
Construct histograms for mothers’ and fathers’ heights and weights from the lung function data set. Describe cases that you consider to be outliers.
For the lung function data set, create a new variable called AGEDIFF = (age of child 1) – (age of child 2) for families with at least two children. Produce a frequency count of this variable.Are there any negative values? Comment.
For the depression data set, determine if any of the variables have observations that do not fall within the ranges given in Table 3.4, codebook for depression data.
From the lung function data set, determine how many families have one child, two children, and three children between the ages of 7 and 18.
From the variables ACUTEILL and BEDDAYS described in Table 3.4, create a single variable that takes on the value 1 if the person has been both bedridden and acutely ill in the last two months and that takes on the value 0 otherwise.
In the Parental HIV data set, the variable LIVWITH (who the adolescent was living with) was coded 1=both parents, 2=one parent, and 3=other. Transform the data so it is coded 1=one parent, 2=two parents, and 3=other using the features available in the statistical package or spreadsheet program you
Consistency checks are sometimes performed to detect possible errors in the data. If a data set included information on sex, age, and use of contraceptive pill, describe a consistency check that could be used for this data set.
Combine the results from the following two questions into a single variable that measures the total number of days the individual has been sick during the time period.: This would allow one variable to be used for analysis involving this data.a. Have you been sick during the last two weeks?Yes, go
For the statistical package you intend to use, describe how you would add data from three more time periods for the same subjects to the depression data set.
Describe the person in the depression data set who has the highest total CESD score.
Transfer or read in a data set that was entered into a spreadsheet program into your statistical software package.
Using the data set entered in the previous problem, delete the P/E variable for the Dow Chemical company and D/E for Stauffer Chemical and Nalco Chemical in a way appropriate for the statistical package you are using. Then, use the missing value features in your statistical package to find the
Enter the data set given in Table 9.1, Chemical companies’ financial performance (Section 9.3), using a data entry program of your choice. Make a codebook for this data set.
Give an example from a field that you are familiar with of an increased sophistication of measuring that has resulted in a measurement that used to be ordinal now being interval.
The Parental HIV data set described in Appendix A includes the following variables: job status of mother (JOBMO, 1=employed, 2=unemployed, and 3=retired/disabled) and mother’s education (EDUMO, 1=did not complete high school, 2=high school diploma/GED, and 3=more than high school). Classify these
Data that are ordinal are often analyzed by methods that Stevens reserved for interval data.Give reasons why thoughtful investigators often do this.
Give an example of nominal, ordinal, interval, and ratio variables from a field of application you are familiar with.
If the RELIG variable described in Table 3.4 of this text was recoded 1 = Catholic, 2 = Protestant, 3 = Jewish, 4 = none, and 5 = other, would this meet the basic empirical operation as defined by Stevens for an ordinal variable?
From a field of statistical application (perhaps your own field of specialty), describe a data set and repeat the procedures described in Problem 2.3.
Repeat Problem 2.3 for the lung cancer data set described in Table 13.1.
For the chronic respiratory study data described in Appendix A, classify each variable according to Stevens’s scale and according to whether it is discrete or continuous. Pose two possible research questions and decide on the appropriate dependent and independent variables.
In a survey of users of a walk-in mental health clinic, data have been obtained on sex, age, household roster, race, education level (number of years in school), family income, reason for coming to the clinic, symptoms, and scores on a screening examination. The investigator wishes to determine
Classify the following types of data by using Stevens’s measurement system: decibels of noise level, father’s occupation, parts per million of an impurity in water, density of a piece of bone, rating of a wine by one judge, net profit of a firm, and score on an aptitude test.
The following table provides the costs for gasoline by month in the U.S. over recent years and the percentage of the cost due to refining, distribution and marketing, taxes, and crude oil. The table is from the U.S. Department of Energy Web site (http://tonto.eia.doe.gov/oog/info/gdu/gaspump.html).
An EWMA chart with and is to be used to monitor a process. Suppose that the process mean is and(a) Assume that What is the ARL without any shift in the process mean? What is the ARL to detect a shift to(b) Assume that Repeat part (a) and comment on your conclusions.
Suppose the average number of defects in a unit is known to be 10.If the mean number of defects in a unit shifts to 14, what is the probability that it will be detected by a U chart on the first sample following the shift(a) if the sample size is n 1?(b) if the sample size is n 4?Use a normal
Suppose the average number of defects in a unit is known to be 8.If the mean number of defects in a unit shifts to 16, what is the probability that it will be detected by a U chart on the first sample following the shift(a) if the sample size is n 4?(b) if the sample size is n 10?Use a normal
Suppose a process has a PCR 2, but the mean is exactly three standard deviations above the upper specification limit. What is the probability of making a product outside the specification limits?
Consider a control chart for individuals with 3-sigma limits. What is the probability that there will not be a signal in three samples? In six samples? In 10 samples?
A process has a target of 0 100 and a standard deviation of 4.Samples of size n 1 are taken every two hours. Use Table 15-9.(a) Suppose the process mean shifts to 102.How many hours of production will occur before the process shift is detected by a CUSUM with h 5 and k 12?(b) It is
Consider an EMWA control chart. The target value for the process is and Use Table 15-10.(a) If the sample size is would you prefer an EWMA chart with and or and to detect a shift in the process mean to on average? Why?(b) If the sample size is increased to which chart in part (a) do you prefer?
Consider the concentration data in Exercise 15-64.Use and assume that the desired process target is 100.(a) Construct an EWMA control chart with Does the process appear to be in control?(b) Construct an EWMA control chart with Compare your results to part (a).(c) If the concentration shifted to
Consider the diameter data in Exercise 15-63.Assume that the desired process target is 10.0 millimeters.(a) Estimate the process standard deviation.(b) Construct an EWMA control chart with Does the process appear to be in control?(c) Construct an EWMA control chart with Compare your results to part
Consider the purity data in Exercise 15-62.Use and assume that the desired process target is 90.(a) Construct an EWMA control chart with Does the process appear to be in control?(b) Construct an EWMA control chart with Compare your results to part (a).(c) Suppose that the next five observations are
Consider an control chart with UCL = 24.802,LCL = 23.792, and n = 3.Suppose the mean shifts to 24.2.(a) What is the probability that this shift will be detected on the next sample?(b) What is the ARL to detect the shift?
An chart uses a subgroup of size three. The center line is at 200, and the upper and lower three-sigma control limits are at 212 and 188, respectively.(a) Estimate the process .(b) Suppose the process mean shifts to 195.Determine the probability that this shift will be detected on the next
Consider the revised control chart in Exercise 15-8 with , UCL 7.443, LCL 5.125, and n 3.Suppose that the mean shifts to 5.5.(a) What is the probability that this shift will be detected on the next sample?(b) What is the ARL after the shift?
Consider an control chart with ,UCL 0.0635, LCL 0.0624, and n 5.Suppose that the mean shifts to 0.0625.X r 0.000924 X r 2.25 X ˆ 2.466 X ˆ 1.40 (a) What is the probability that this shift will be detected on the next sample?(b) What is the ARL after the shift?
Consider an control chart with , UCL 17.40, LCL 12.79, and n 3.Suppose that the mean shifts to 13.(a) What is the probability that this shift will be detected on the next sample?(b) What is the ARL after the shift?
Consider an control chart with , UCL 37.404, LCL 30.780, and n 5.Suppose that the mean shifts to 36.(a) What is the probability that this shift will be detected on the next sample?(b) What is the ARL after the shift?
Consider an control chart with , UCL 21.71, LCL 18.29, and n 6.Suppose that the mean shifts to 17.(a) What is the probability that this shift will be detected on the next sample?(b) What is the ARL after the shift?
Consider an control chart with , UCL 242.780, LCL 203.220, and n 5.Suppose that the mean shifts to 210.(a) What is the probability that this shift will be detected on the next sample?(b) What is the ARL after the shift?
Consider an control chart with , UCL 14.708, LCL 14.312, and n 5.Suppose that the mean shifts to 14.6.(a) What is the probability that this shift will be detected on the next sample?(b) What is the ARL after the shift?
Consider the control chart in Fig. 15-3.Suppose that the mean shifts to 74.010 millimeters.X XEXERCISES FOR SECTION 15-7(a) What is the probability that this shift will be detected on the next sample?(b) What is the ARL after the shift?

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Applied Statistics And Probability For Engineers 5th Edition Douglas C. Montgomery, George C. Runger - Solutions

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