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applied statistics and multivariate

Questions and Answers of Applied Statistics And Multivariate

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,
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)
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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 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,
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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)
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
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
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
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
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
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)
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
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
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 (
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
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
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
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
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
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
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
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
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
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,
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
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
Consider the film speed data in Exercise 10-22.(a) Test H0: 2 1 2 2 versus using 0.02.(b) Suppose that one population standard deviation is 50%larger than the other. Is the sample size n1
Consider the weight of paper data from Technometrics in Exercise 10-28.Is there evidence that the variance of the weight measurement differs between the sheets of paper? Use. Explain how this test
Reconsider the overall distance data for golf balls in Exercise 10-29.Is there evidence to support the claim that the standard deviation of overall distance is the same for both brands of balls (use
Exercise 10-24 presented measurements of plastic coating thickness at two different application temperatures.Test H0: 2 1 2 2 against using 0.01.
Consider the melting-point data in Exercise 10-21.Do the sample data support a claim that both alloys have the same variance of melting point? Use 0.05 in reaching your conclusion.
Consider the gear impact strength data in Exercise 10-20.Is there sufficient evidence to conclude that the variance of impact strength is different for the two suppliers? Use 0.05.
Consider the foam data in Exercise 10-16.Construct the following:(a) A 90% two-sided confidence interval on 2 12 2.(b) A 95% two-sided confidence interval on 2 12 2.Comment on the comparison of
A study was performed to determine whether men and women differ in their repeatability in assembling components on printed circuit boards. Random samples of 25 men and 21 women were selected, and
Consider the hypothesis test H0 :2 1 2 2 against H0 :2 1 2 2.Suppose that the sample sizes are and, and that and . Use . Test the hypothesis and explain how the test could be conducted with a
Consider the hypothesis test H0 :2 1 2 2 against H1 :2 1 2 2.Suppose that the sample sizes are and, and that and . Use . Test the hypothesis and explain how the test could be conducted with a
Repeat Exercise 10-47 using the Wilcoxon signedrank test. State carefully what hypothesis is being tested and how it differs from the one tested in Exercise 10-47.

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