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applied statistics and multivariate
Applied Statistics And Probability For Engineers 5th Edition Douglas C. Montgomery, George C. Runger - Solutions
Consider the gasoline mileage data in Exercise 12-7.(a) Find 99% confidence intervals on the regression coefficients.(b) Find a 99% confidence interval on the mean of Y for the regressor values in the first row of data.(c) Fit a new regression model to these data using cid, etw, and axle as the
Consider the heat treating data from Exercise 12-10.(a) Find 95% confidence intervals on the regression coefficients.(b) Find a 95% confidence interval on mean PITCH when TEMP 1650, SOAKTIME 1.00, SOAKPCT 1.10, DIFFTIME 1.00, and DIFFPCT 0.80.(c) Fit a model to PITCH using regressors x1
Consider the NFL data in Exercise 12-17.(a) Find 95% confidence intervals on the regression coefficients.(b) What is the estimated standard error of when the percentage of completions is 60%, the percentage of TDs is 4%, and the percentage of interceptions is 3%.(c) Find a 95% confidence interval
Consider the stack loss data in Exercise 12-16.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 95% confidence interval on mean stack loss when and(c) Calculate a prediction interval on stack loss for the same values of the regressors used in the previous
Consider the regression model fit to the grey range modulation data in Exercise 12-15.Use the useful range as the response.(a) Calculate 99% confidence intervals on each regression coefficient.(b) Calculate a 99% confidence interval on mean useful range when and(c) Calculate a prediction interval
Consider the regression model fit to the nisin extraction data in Exercise 12-14.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 95% confidence interval on mean nisin extraction when and(c) Calculate a prediction interval on nisin extraction for the same values
Consider the regression model fit to the coal and limestone mixture data in Exercise 12-13.Use density as the response.(a) Calculate 90% confidence intervals on each regression coefficient.(b) Calculate a 90% confidence interval on mean density when the dielectric and the loss factor (c) Calculate
Consider the regression model fit to the arsenic data in Exercise 12-12.Use arsenic in nails as the response and age, drink use, and cook use as the regressors.(a) Calculate 99% confidence intervals on each regression coefficient.(b) Calculate a 99% confidence interval on mean arsenic concentration
Consider the regression model fit to the X-ray inspection data in Exercise 12-11.Use rads as the response.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 99% confidence interval on mean rads at 15 milliamps and 1 second on exposure time.(c) Calculate a 99%
Consider the wire bond pull strength data in Exercise 12-8.(a) Find 95% confidence interval on the regression coefficients.(b) Find a 95% confidence interval on mean pull strength when x2 20, x3 30, x4 90, and x5 2.0.(c) Find a 95% prediction interval on pull strength when x2 20, x3 30,
Consider the bearing wear data in Exercise 12-19.(a) Find 99% confidence intervals on 1 and 2.(b) Recompute the confidence intervals in part (a) after the interaction term x1x2 is added to the model. Compare the lengths of these confidence intervals with those computed in part (a). Do the lengths
Consider the electric power consumption data in Exercise 12-6.(a) Find 95% confidence intervals on 1, 2, 3, and 4.(b) Find a 95% confidence interval on the mean of Y when x1 75, x2 24, x3 90, and x4 98.(c) Find a 95% prediction interval on the power consumption when x1 75, x2 24, x3
Consider the semiconductor data in Exercise 12-9.(a) Find 99% confidence intervals on the regression coefficients.(b) Find a 99% prediction interval on HFE when x1 14.5, x2 220, and x3 5.0.(c) Find a 99% confidence interval on mean HFE when x1 14.5, x2 220, and x3 5.0.
Consider the soil absorption data in Exercise 12-2.(a) Find 95% confidence intervals on the regression coefficients.(b) Find a 95% confidence interval on mean soil absorption index when x1 200 and x2 50.(c) Find a 95% prediction interval on the soil absorption index when x1 200 and x2 50.
Consider the regression model fit to the shear strength of soil in Exercise 12-1.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 95% confidence interval on mean strength when feet and(c) Calculate 95% prediction interval on strength for the same values of the
Data from a hospital patient satisfaction survey were presented in Exercise 12-5.(a) Fit a regression model using only the patient age and severity regressors. Test the model from this exercise for significance of regression. What conclusions can you draw if 0.05?What if 0.01?(b) Test the
Data from a hospital patient satisfaction survey were presented in Exercise 12-5.(a) Test the model from this exercise for significance of regression.What conclusions can you draw if 0.05? What if 0.01?(b) Test the contribution of the individual regressors using the t-test. Does it seem
Data on National Hockey League team performance was presented in Exercise 12-18.(a) Test the model from this exercise for significance of regression using 0.05. What conclusions can you draw?(b) Use the t-test to evaluate the contribution of each regressor to the model. Does it seem that all
Consider the bearing wear data in Exercise 12-19.(a) For the model with no interaction, test for significance of regression using 0.05. What is the P-value for this test? What are your conclusions?(b) For the model with no interaction, compute the t-statistics for each regression coefficient.
Exercise 12-10 presents data on heat treating gears.(a) Test the regression model for significance of regression.Using 0.05, find the P-value for the test and draw conclusions.(b) Evaluate the contribution of each regressor to the model using the t-test with 0.05.(c) Fit a new model to the
Consider the NFL data in Exercise 12-17.(a) Test for significance of regression using 0.05. What is the P-value for this test?(b) Conduct the t-test for each regression coefficient. Using 0.05, what conclusions can you draw about the variables in this model?(c) Find the amount by which the
Consider the regression model fit to the stack loss data in Exercise 12-16.Use stack loss as the response.(a) Test for significance of regression using What is the P-value for this test?(b) Construct a t-test on each regression coefficient. What conclusions can you draw about the variables in this
Consider the regression model fit to the grey range modulation data in Exercise 12-15.Use the useful range as the response.(a) Test for significance of regression using What is the P-value for this test?(b) Construct a t-test on each regression coefficient. What conclusions can you draw about the
Consider the regression model fit to the nisin extraction data in Exercise 12-14.Use nisin extraction as the response.(a) Test for significance of regression using What is the P-value for this test?(b) Construct a t-test on each regression coefficient. What conclusions can you draw about the
Consider the regression model fit to the X-ray inspection data in Exercise 12-11.Use rads as the response.(a) Test for significance of regression using What is the P-value for this test?(b) Construct a t-test on each regression coefficient. What conclusions can you draw about the variables in this
Consider the regression model fit to the arsenic data in Exercise 12-12.Use arsenic in nails as the response and age, drink use, and cook use as the regressors.(a) Test for significance of regression using What is the P-value for this test?(b) Construct a t-test on each regression coefficient. What
Reconsider the semiconductor data in Exercise 12-9.(a) Test for significance of regression using 0.05. What conclusions can you draw?(b) Calculate the t-test statistic and P-value for each regression coefficient. Using 0.05, what conclusions can you draw?
Consider the wire bond pull strength data in Exercise 12-8.(a) Test for significance of regression using 0.05. Find the P-value for this test. What conclusions can you draw?(b) Calculate the t-test statistic for each regression coefficient. Using 0.05, what conclusions can you draw?Do all
Consider the gasoline mileage data in Exercise 12-7.(a) Test for significance of regression using 0.05. What conclusions can you draw?(b) Find the t-test statistic for each regressor. Using 0.05, what conclusions can you draw? Does each regressor contribute to the model?
Consider the electric power consumption data in Exercise 12-6.(a) Test for significance of regression using 0.05. What is the P-value for this test?(b) Use the t-test to assess the contribution of each regressor to the model. Using 0.05, what conclusions can you draw?
A regression model Y 0 1x1 2x2 3x3 has been fit to a sample of n 25 observations. The calculated t-ratios are as follows: for 1, t0 4.82, for 2, t0 8.21 and for 3, t0 0.98.(a) Find P-values for each of the t-statistics.(b) Using 0.05, what conclusions can you draw about the regressor
Consider the absorption index data in Exercise 12-2.The total sum of squares for y is SST 742.00.(a) Test for significance of regression using 0.01. What is the P-value for this test?(b) Test the hypothesis H0: 1 0 versus H1: 1 0 using 0.01. What is the P-value for this test?(c) What conclusion
Use stepwise regression and other model building techniques to select the appropriate set of variables for a regression model
Use indicator variables to model categorical regressors
Build regression models with polynomial terms
Use the regression model to estimate the mean response and to make predictions and to construct confidence intervals and prediction intervals
Test hypotheses and construct confidence intervals on the regression coefficients
Assess regression model adequacy
Understand how the method of least squares extends to fitting multiple regression models
Use multiple regression techniques to build empirical models to engineering and scientific data
Consider the following (x, y) data. Calculate the correlation coefficient. Graph the data and comment on the relationship between x and y. Explain why the correlation coefficient does not detect the relationship between x and y.
Refer to the NFL quarterback ratings data in Exercise 11-3.(a) Estimate the correlation coefficient between the ratings and the average yards per attempt.(b) Test the hypothesis versus using. What is the P-value for this test?(c) Construct a 95% confidence interval for .(d) Test the hypothesis
The monthly absolute estimate of global (land and ocean combined) temperature indexes (degrees C) in 2000 and 2001 are (source: http://www.ncdc.noaa.gov/oa/climate/):2000: 12.28, 12.63, 13.22, 14.21, 15.13, 15.82, 16.05, 16.02, 15.29, 14.29, 13.16, 12.47 2001: 12.44, 12.55, 13.35, 14.22, 15.28,
The final test and exam averages for 20 randomly selected students taking a course in engineering statistics and a course in operations research follow. Assume that the final averages are jointly normally distributed.(a) Find the regression line relating the statistics final average to the OR final
The following data gave X the water content of snow on April 1 and Y the yield from April to July (in inches) on the Snake River watershed in Wyoming for 1919 to 1935. (The data were taken from an article in Research Notes, Vol. 61, 1950, Pacific Northwest Forest Range Experiment Station,
A random sample of 50 observations was made on the diameter of spot welds and the corresponding weld shear strength.(a) Given that r 0.62, test the hypothesis that 0, using 0.01. What is the P-value for this test?(b) Find a 99% confidence interval for .(c) Based on the confidence interval in
A random sample of n 25 observations was made on the time to failure of an electronic component and the temperature in the application environment in which the component was used.(a) Given that r 0.83, test the hypothesis that 0, using 0.05. What is the P-value for this test?(b) Find a 95%
Suppose data are obtained from 20 pairs of (x, y) and the sample correlation coefficient is 0.75.(a) Test the hypothesis that against with. Calculate the P-value.(b) Test the hypothesis that against with . Calculate the P-value.(c) Construct a 95% one-sided confidence interval for the correlation
Suppose data is obtained from 20 pairs of (x, y) and the sample correlation coefficient is 0.8.(a) Test the hypothesis that against with. Calculate the P-value.(b) Test the hypothesis that against with . Calculate the P-value.(c) Construct a 95% two-sided confidence interval for the correlation
Consider the rocket propellant data in Exercise 11-11.Calculate the standardized residuals for these data. Does this provide any helpful information about the magnitude of the residuals?
Consider the data in Exercise 11-7 on y green liquor Na2S concentration and x paper machine production.Suppose that a 14th sample point is added to the original data, where y14 59 and x14 855.(a) Prepare a scatter diagram of y versus x. Fit the simple linear regression model to all 14
Consider the rocket propellant data in Exercise 11-11.(a) Calculate R2 for this model. Provide an interpretation of this quantity.(b) Plot the residuals on a normal probability scale. Do any points seem unusual on this plot?(c) Delete the two points identified in part (b) from the sample and fit
An article in the Journal of the American Statistical Association [“Markov Chain Monte Carlo Methods for Computing Bayes Factors: A Comparative Review” (2001, Vol. 96, pp. 1122–1132)] analyzed the tabulated data on compressive strength parallel to the grain versus resin-adjusted density for
Refer to Exercise 11-10, which presented data on chloride concentration y and roadway area x.(a) What proportion of the total variability in chloride concentration is accounted for by the regression model?(b) Plot the residuals versus and versus x. Interpret these plots.(c) Prepare a normal
Refer to Exercise 11-8, which presented data on blood pressure rise y and sound pressure level x.(a) What proportion of total variability in blood pressure rise is accounted for by sound pressure level?(b) Prepare a normal probability plot of the residuals from this least squares model. Interpret
Exercise 11-9 presents data on wear volume y and oil viscosity x.(a) Calculate R2 for this model. Provide an interpretation of this quantity.(b) Plot the residuals from this model versus and versus x.Interpret these plots.(c) Prepare a normal probability plot of the residuals. Does the normality
Refer to the gasoline mileage data in Exercise 11-6.(a) What proportion of total variability in highway gasoline mileage performance is accounted for by engine displacement?(b) Plot the residuals versus and yˆ x, and comment on the graphs(c) Prepare a normal probability plot of the residuals. Does
Refer to the data in Exercise 11-5 on y steam usage and x average monthly temperature.(a) What proportion of total variability is accounted for by the simple linear regression model?(b) Prepare a normal probability plot of the residuals and interpret this graph.(c) Plot residuals versus and x. Do
Refer to the data in Exercise 11-4 on house selling price y and taxes paid x.(a) Find the residuals for the least squares model.(b) Prepare a normal probability plot of the residuals and interpret this display(c) Plot the residuals versus and versus x. Does the assumption of constant variance seem
Refer to the NFL quarterback ratings data in Exercise 11-3.(a) Calculate R2 for this model and provide a practical interpretation of this quantity.(b) Prepare a normal probability plot of the residuals from the least squares model. Does the normality assumption seem to be satisfied?(c) Plot the
Refer to the compressive strength data in Exercise 11-1.Use the summary statistics provided to calculate R2 and provide a practical interpretation of this quantity.
Refer to the data in Exercise 11-13 on oxygen demand. Find a 99% confidence interval on each of the following:(a)(b)(c) Find a 95% confidence interval on mean BOD when the time is 8 days.
Refer to the data in Exercise 11-12 on the microstructure of zirconia. Find a 95% confidence interval on each of the following:(a) Slope (b) Intercept(c) Mean length when(d) Find a 95% prediction interval on length when Explain why this interval is wider than the interval in part (c).
Refer to the data in Exercise 11-11 on rocket motor shear strength y and propellant age x. Find a 95% confidence interval on each of the following:(a) Slope 1 (b) Intercept 0(c) Mean shear strength when age x 20 weeks(d) Find a 95% prediction interval on shear strength when age x 20 weeks.
Exercise 11-10 presented data on chloride concentration y and roadway area x on watersheds in central Rhode Island. Find a 99% confidence interval on each of the following:(a) 1 (b) 0(c) Mean chloride concentration when roadway area x 1.0%(d) Find a 99% prediction interval on chloride concentration
Refer to the data in Exercise 11-9 on y wear volume of mild steel and x oil viscosity. Find a 95% confidence interval on each of the following:(a) Intercept (b) Slope(c) Mean wear when oil viscosity x 30
Exercise 11-8 presented data on y blood pressure rise and x sound pressure level. Find a 95% confidence interval on each of the following:(a) 1 (b) 0(c) Mean blood pressure rise when the sound pressure level is 85 decibels(d) Find a 95% prediction interval on blood pressure rise when the sound
Consider the data in Exercise 11-7 on y green liquor Na2S concentration and x production in a paper mill. Find a 99% confidence interval on each of the following:(a) 1 (b) 0(c) Mean Na2S concentration when production x 910 tonsday(d) Find a 99% prediction interval on Na2S concentration when x 910
Exercise 11-6 presented gasoline mileage performance for 21 cars, along with information about the engine displacement. Find a 95% confidence interval on each of the following:(a) Slope (b) Intercept(c) Mean highway gasoline mileage when the engine displacement is x 150 in3(d) Construct a 95%
Exercise 11-5 presented data on y steam usage and x monthly average temperature(a) Find a 99% confidence interval for 1.(b) Find a 99% confidence interval for 0.(c) Find a 95% confidence interval on mean steam usage when the average temperature is .(d) Find a 95% prediction interval on steam
Refer to the data on y house selling price and x taxes paid in Exercise 11-4.Find a 95% confidence interval on each of the following:(a) 1 (b) 0(c) Mean selling price when the taxes paid are x 7.50(d) Compute the 95% prediction interval for selling price when the taxes paid are x 7.50.
Refer to the NFL quarterback ratings data in Exercise 11-3.Find a 95% confidence interval on each of the following:(a) Slope(b) Intercept(c) Mean rating when the average yards per attempt is 8.0(d) Find a 95% prediction interval on the rating when the average yards per attempt is 8.0.
Exercise 11-2 presented data on roadway surface temperature x and pavement deflection y. Find a 99% confidence interval on each of the following:(a) Slope (b) Intercept(c) Mean deflection when temperature(d) Find a 99% prediction interval on pavement deflection when the temperature is .
Refer to the data in Exercise 11-1 on y intrinsic permeability of concrete and x compressive strength. Find a 95% confidence interval on each of the following:(a) Slope (b) Intercept(c) Mean permeability when x 2.5(d) Find a 95% prediction interval on permeability when x 2.5. Explain why this
Consider the data from Exercise 11-10 on y chloride concentration in surface streams and x roadway area.(a) Test the hypothesis H0: 1 0 versus H1: 1 0 using the analysis of variance procedure with 0.01.(b) Find the P-value for the test in part (a).(c) Estimate the standard errors of andˆ0 .
Consider the data from Exercise 11-11, on y shear strength of a propellant and x propellant age.(a) Test for significance of regression with 0.01. Find the P-value for this test.(b) Estimate the standard errors of and(c) Test H0: 1 30 versus H1: 1 30 using 0.01.What is the P-value for this
Consider the data from Exercise 11-8 on y blood pressure rise and x sound pressure level.(a) Test for significance of regression using 0.05. What is the P-value for this test?(b) Estimate the standard errors of the slope and intercept.(c) Test H0: 0 0 versus H1: 0 0 using 0.05. Find the P-value
Consider the data from Exercise 11-7 on y green liquor Na2S concentration and x production in a paper mill.(a) Test for significance of regression using 0.05. Find the P-value for this test.(b) Estimate the standard errors of the slope and intercept.(c) Test H0: 0 0 versus H1: 0 0 using 0.05.
Consider the data from Exercise 11-6 on y highway gasoline mileage and x engine displacement.(a) Test for significance of regression using 0.01. Find the P-value for this test. What conclusions can you reach?(b) Estimate the standard errors of the slope and intercept.(c) Test H0: 1 0.05 versus
Consider the data from Exercise 11-5 on y steam usage and x average temperature.(a) Test for significance of regression using 0.01. What is the P-value for this test? State the conclusions that result from this test.(b) Estimate the standard errors of the slope and intercept.(c) Test the
Use simple transformations to achieve a linear regression model
Apply the correlation model
Use the regression model to make a prediction of a future observation and construct an appropriate prediction interval on the future observation
Test statistical hypotheses and construct confidence intervals on regression model parameters
Analyze residuals to determine if the regression model is an adequate fit to the data or to see if any underlying assumptions are violated
Understand how the method of least squares is used to estimate the parameters in a linear regression model
Use simple linear regression for building empirical models to engineering and scientific data
In some situations involving proportions, we are interested in the ratio p1p2 rather than the difference p1 p2. Let . We can show that ln( ) has an approximate normal distribution with the mean ( )and variance(a) Use the information above to derive a large-sample confidence interval for ln.(b)
Construct a data set for which the paired t-test statistic is very large, indicating that when this analysis is used the two population means are different, but t0 for the two-sample t-test is very small so that the incorrect analysis would indicate that there is no significant difference between
Suppose that we wish to test H0: 1 2 versus H1: 1 2, where 2 1 and 2 2 are known. The total sample size N is to be determined, and the allocation of observations to the two populations such that n1 n2 N is to be made on the basis of cost. If the cost of sampling for populations 1 and 2 are C1
A fuel-economy study was conducted for two German automobiles, Mercedes and Volkswagen. One vehicle of each brand was selected, and the mileage performance was observed for 10 tanks of fuel in each car. The data are as follows (in miles per gallon):(a) Construct a normal probability plot of each of
Consider the fire-fighting foam expanding agents investigated in Exercise 10-16, in which five observations of each agent were recorded. Suppose that, if agent 1 produces a mean expansion that differs from the mean expansion of agent 1 by 1.5, we would like to reject the null hypothesis with
A manufacturer of a new pain relief tablet would like to demonstrate that its product works twice as fast as the competitor’s product. Specifically, the manufacturer would like to test where 1 is the mean absorption time of the competitive product and 2 is the mean absorption time of the new
In a random sample of 200 Phoenix residents who drive a domestic car, 165 reported wearing their seat belt regularly, while another sample of 250 Phoenix residents who drive a foreign car revealed 198 who regularly wore their seat belt.(a) Perform a hypothesis-testing procedure to determine if
Consider Supplemental Exercise 10-78.Suppose that prior to collecting the data, you decide that you want the error in estimating 1 2 by to be less than 1.5 psi. Specify the sample size for the following percentage confidence:(a) 90%(b) 98%(c) Comment on the effect of increasing the percentage
The Salk polio vaccine experiment in 1954 focused on the effectiveness of the vaccine in combating paralytic polio. Because it was felt that without a control group of children there would be no sound basis for evaluating the efficacy of the Salk vaccine, the vaccine was administered to one group,
A random sample of 500 adult residents of Maricopa County found that 385 were in favor of increasing the highway speed limit to 75 mph, while another sample of 400 adult residents of Pima County found that 267 were in favor of the increased speed limit.(a) Do these data indicate that there is a
Two different types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored. Two random samples, each of size 300, are selected, and 15 defective parts are found in the sample from machine 1 while 8 defective parts
In the 2004 presidential election, exit polls from the critical state of Ohio provided the following results: For respondents with college degrees, 53% voted for Bush and 46%voted for Kerry. There were 2020 respondents.(a) Is there a significant difference in these proportions? Use. What is the
Consider the etch rate data in Exercise 10-19.(a) Test the hypothesis H0: 2 1 2 2 against H1: 2 1 2 2using 0.05, and draw conclusions.(b) Suppose that if one population variance is twice as large as the other, we want to detect this with probability at least 0.90 (using 0.05). Are the
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