Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions

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Find det (P) in Prob. 18 and hence demonstrate Theorem 1.8.4.
Find the entries $x_i$ in the matrix P so that P is an orthogonal matrix where P=$$\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & -1 & -1 \\1 & -1 & 1 & -1 \\x_1 & x_2 & x_3 & x_4\end{bmatrix}$$
Use the matrix A in Prob. 16 and the result of Prob. 16 to transform the quadratic form x'Ax to y; - iL that is, find C such that y = Cx.
Find a nonsingular matrix C such that$$C^{'}AC = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{bmatrix}.$$
For the matrix A where$$A = \begin{bmatrix} 1 & -1 & 0 \\ 1 & 1 & 2 \\ 2 & 0 & 2 \end{bmatrix},$$find a 3 x 3 matrix X of rank 3 - r such that AX = 0 (r is the rank of A).
For the matrix A where$$A = \begin{bmatrix} 1 & 2 & -1 & 1 \\ 2 & 1 & 0 & 3 \\ 0 & -3 & 2 & 1 \\ -3 & 0 & -1 & -5 \end{bmatrix}$$find matrices P and Q such that$$PAQ = \begin{bmatrix} I_r & 0 \\ 0 & 0 \end{bmatrix},$$where r is the rank of A. This demonstrates Theorem 1.6.8.
Find a set of elementary matrices such that A in Prob. 10 is equal to the product of these elementary matrices, thus demonstrating Theorem 1.6.5.
Use the results of Prob. 9 and 10 to find A-1.
In Prob. 9, find the inverse of each of the eight elementary transformation matrices.
If A in Prob. 9 is defined by
Suppose you want to perform the following operations on a 3 x 3 matrix, A:(1) Interchange the first and third rows.(2) Interchange the first and third columns.(3) Multiply the first row by -2 and add the result to the third row.(4) Multiply the first column by -2 and add the result to the third
Consider the matrices A, B, and C, where A is defined as in Prob. 1 and$$B = \begin{bmatrix} 2 & 3 & 1 \\ 2 & 1 & 1 \\ 1 & 0 & 3 \end{bmatrix},$$$$C = \begin{bmatrix} 3 & 2 & 1 \\ 2 & 1 & 1 \\ 1 & 0 & 3 \end{bmatrix}$$.Note that A, B, and C are identical except for the first row, and for that row
Use Prob. 5 to demonstrate Theorem 1.5.11.
Use the results of Prob. 5 and Theorem 1.5.9 to evaluate det (A).
In Prob. 4, find *A*11, *A*12, *A*13, where *A**ij* is the cofactor of *a**ij*.
In Prob. 1, find *m*11, *m*12, *m*13, where *m**ij* is the minor of *a**ij*.
In Prob. 1, find (AT)-1 and (A-1)T, and hence demonstrate Theorem 1.4.7.
In Prob. 1, find A-1.
Find the determinant of the matrix A where$$A = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 1 & 1 \\ 1 & 0 & 3 \end{bmatrix}$$.
Income by Age. The data from Problem 34 on the annual incomes, in thousands of dollars, for independent simple random samples of 100 employed persons in each of four age groups.
Weight Loss and Leg Power. The data from Problem 33 on the Maximum Nottingham leg power of three weight-loss groups of older men.
Weight Loss and BMI. The data from Problem 32 on the BMIs of three weight-loss groups of older men.
Income by Age. The U.S. Census Bureau collects information on incomes of employed persons and publishes the results in Historical Income Tables. Independent simple random samples of 100 employed persons in each of four age groups gave the data on annual income, in thousands of dollars, presented on
Weight Loss and Leg Power. Another characteristic compared in the hip bone density study discussed in Problem 32 was Maximum Nottingham leg power, in watts. On the WeissStats site, we provide the leg-power data for the three groups, based on the results obtained by the researchers.
Weight Loss and BMI. In the paper “Voluntary Weight Reduction in Older Men Increases Hip Bone Loss: The Osteoporotic Fractures in Men Study” (Journal of Clinical Endocrinology &Metabolism, Vol. 90, Issue 4, pp. 1998–2004), K. Ensrud et al. reported on the effect of voluntary weight reduction
Smoking and Cotinine. Refer to Problem 30. Decide whether conducting a Kruskal–Wallis test on the data is reasonable.
Smoking and Cotinine. Smoking during pregnancy is hazardous to both the mother and baby. Passive smoking, or inhalation of second-hand smoke, is also a concern. In the article “Detection of Cotinine in Neonate Meconium as a Marker for Nicotine Exposure in Utero” (Eastern Mediterranean Health
Foot-pressure Angle. Genu valgum, commonly known as“knee-knock,” is a condition in which the knees angle in and touch one another when standing. Genu varum, commonly known as “bowlegged,” is a condition in which the knees angle out and the legs bow when standing. In the article “Frontal
Refer to Problem 24.a. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference in mean death and injured toll in earthquakes? Use the Kruskal–Wallis procedure to perform the required hypothesis test.b. The hypothesis test in part (a) was done in Problem
Refer to Problem 24.a. Apply the Tukey multiple-comparison method to the data. Use a family confidence level of 0.95.b. Interpret your results from part (a).* Earthquake.
Earthquake. Refer to Problem 24. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference in mean injured and death toll in the earthquakes? Use one-way ANOVA to perform the required hypothesis test. (Note: T1 = 845.443, T2 =380.395, and x 2 =
Earthquake. Refer to Problem 24.a. Obtain individual normal probability plots and the standard deviations of the samples.b. Perform a residual analysis.c. Decide whether presuming that the assumptions of normal populations and equal standard deviations are met is reasonable.
Earthquake. On the page “List of 21st-century earthquakes”on Wikipedia, there’s information of the earthquakes and the fatalities that happened in the world in the 21st century. A random sample out of all the earthquakes is given along with the fatalities caused in the following table. The
Consider the following hypothetical samples.A B C 1 0 3 3 6 12 5 2 6 5 3 2a. Obtain the sample mean and sample variance of each of the three samples.b. Obtain SST, SSTR, and SSE by using the defining formulas and verify that the one-way ANOVA identity holds.c. Obtain SST, SSTR, and SSE by using the
Suppose that you want to compare the means of three populations by using the Tukey multiple-comparison procedure. If the sample sizes are 5, 6, and 6, determine the parameters for the appropriate q-curve.
On what distribution does the Tukey multiple-comparison procedure rely?
Explain the difference between the individual confidence level and the family confidence level. Which confidence level is appropriate for multiple comparisons? Explain your answer.
Explain in detail the purpose of conducting a multiple comparison.*
For a one-way ANOVA,a. identify one purpose of one-way ANOVA tables.b. construct a generic one-way ANOVA table.*
In one-way ANOVA,a. list and interpret the three sums of squares.b. state the one-way ANOVA identity and interpret its meaning with regard to partitioning the total variation among all the data.
For what is one-way ANOVA used?
perform a Kruskal–Wallis test.
perform a multiple comparison by using the Tukey method.
use the q-tables, Tables IX and X in Appendix A.
perform a one-way ANOVA test.
construct a one-way ANOVA table.
compute the mean squares and the F-statistic for a one-way ANOVA.
obtain the sums of squares for a one-way ANOVA by using the computing formulas.
obtain the sums of squares for a one-way ANOVA by using the defining formulas.
state and check the assumptions required for a one-way ANOVA.
explain the essential ideas behind a one-way ANOVA.
use the F-table, Table VIII in Appendix A.
use and understand the formulas in this chapter.
Vehicle Miles. In this section, we illustrated the Kruskal–Wallis test with data on miles driven by samples of cars, buses, and trucks. The value of the test statistic K was computed on page 751 to be 9.930, whereas on page 753, we found its value to be 9.923.a. Explain the discrepancy between
Artificial Teeth: Wear. The data from Exercise 16.58 on the volume of material worn away, in cubic millimeters, among three different materials for making artificialteeth. Use a 5% significancelevel.
Rock Sparrows. The data from Exercise 16.57 on the number of minutes per hour that male Rock Sparrows sang in the vicinity of the nests after patch-size manipulations were done on three different groups of females. Use a 1% significance level.
Ground Water. The data from Exercise 16.56 on the concentrations, in milligrams per liter, of each of four chemicals among three different wells. Use a 1% significance level.
Monthly Rents. The data from Exercise 16.55 on monthly rents, in dollars, for independent random samples of newly completed apartments in the four U.S. regions. Use a 5% significance level.
Empty Stomachs. The data from Exercise 16.54 on the proportions of fish with empty stomachs among four species in African waters. Use a 1% significance level.
Theraphosaidea. Following are the data from Exercise 16.51 on Femur length of the four legs of the new genus of Theraphosaidea.Leg I Leg II Leg III Leg IV 7.72 6.74 6.44 9.16 6.38 5.39 5.82 8.37 8.59 7.36 6.92 10.0 7.36 6.22 6.72 9.69 6.93 6.98 6.01 8.71a. Use the Kruskal-Wallis test to decide, at
Book Review. Following are the data from Exercise 16.48 on the number of pages for random samples of books in five rating groups.1* 2* 3* 4* 5*382 560 384 325 360 391 343 458 390 298 335 512 409 304 272 368 329 309 240 368 400 391 374 306 320 372 367 459 169 326a. Use the Kruskal-Wallis test to
Spider Mites. The reproduction capability of spider mites infected with a bacteria called Cardinium was studied in the article“Cardinium Symbionts Cause Cytoplasmic Incompatibility in Spider Mites” (Heredity, Vol. 98, No. 1, pp. 13–20) by T. Gotoh et al. Infected mites were crossed with mites
Free Lunch. In the publication “What Makes a High School Great?” (Newsweek, May 8, 2006, pp. 50–60), B. Kantrowitz and P. Wingert looked for America’s best high schools. One relevant variable is the percentage of the student body that is eligible for free and reduced lunches, an indicator
Home Size. The U.S. Census Bureau publishes information on the sizes of housing units in Current Housing Reports. Independent random samples of single-family detached homes (including mobile homes) in the four U.S. regions yielded the following data on square footage.Northeast Midwest South West
Ages of Car Buyers. Information on characteristics of new-car buyers appears in Buyers of New Cars, a publication of Newsweek, Inc. Independent random samples of new-car buyers yielded the data on age of purchaser, in years, by origin of car purchased, shown in the following table. Do the data
TV-Commercial Placement. In the article “Violence and Sex Impair Memory for Television Ads” (Journal of Applied Psychology, Vol. 87, No. 3, pp. 557–564), B. Bushman and A. Bonacci studied whether the type of television program in which commercials are placed affects a viewer’s ability to
Entertainment Expenditures. The Bureau of Labor Statistics conducts surveys on consumer expenditures for various types of entertainment and publishes its findings in Consumer Expenditure Survey. Independent random samples yielded the following data, in dollars, on last year’s expenditures for
For a Kruskal–Wallis test to compare five population means, what is the approximate distribution of K?
To decide whether the variation among sample mean ranks is large enough to warrant rejection of the null hypothesis of equal population means, we use the ratio of to . This ratio is called the -statistic.
The measure of total variation of all the ranks is the of all the ranks, which can be expressed as /(n − 1), where is the total sum of squares computed for the ranks.
The measure of variation among the sample mean ranks is computed for the .
Fill in the blank: If the null hypothesis of equal population means is true, the sample mean ranks should be roughly .Regarding a Kruskal–Wallis test, fill in the blanks in each of Exercises 16.126–16.128.
Energy Consumption. Apply Table 16.11 on page 745 and your answer from Exercise 16.120 to determine the remaining six confidence intervals for the differences between the energy consumption means.
In Step 3 of Procedure 16.2, we obtain confidence intervals only when i < j. Explain how to determine the remaining confidence intervals from those obtained.
Explain why the family confidence level, not the individual confidence level, is the appropriate level for comparing all population means simultaneously.
Prolonging Life. The data from Exercise 16.72 on the survival times, in days, among samples of patients in advanced stages of cancer, grouped by the affected organ, who were given a vitamin C supplement.Extending the Concepts and Skills
Sickle Cell Disease. The data from Exercise 16.71 on the steady-state hemoglobin levels of patients with three different types of sickle cell disease.
Magazine Ads. The data from Exercise 16.70 on the number of words of three syllables or more in advertisements from magazines of three different educational levels.
Book Prices. The data from Exercise 16.69 on book prices, in dollars, for independent random samples of hardcover books in law, science, medicine, and technology.
in months, of independent simple random samples of released prisoners among five different offense categories.
Doing Time. The data from Exercise
Cuckoo Care. The data from Exercise 16.67 on the lengths, in millimeters, of cuckoo eggs found in the nests of six bird species.
on weight losses, in kilograms, over a 1-year period of four popular diets. Recall that negative losses are gains and that WW = Weight Watchers.
Popular Diets. The data from Exercise
Fish of Lake Laengelmaevesi. The data from Exercise 16.65 on weight (in grams) and length (in centimeters) from the nose to the beginning of the tail for four species of fish caught in Lake Laengelmaevesi, Finland. Consider both the weight and length data for possible analysis.
Daily TV Viewing Time. The data from Exercise 16.64 on the daily TV viewing times, in hours, of independent simple random samples of men, women, teens, and children.
Starting Salaries. Following are summary statistics from Exercise 16.63 on starting salaries, in thousands of dollars, for samples of bachelor’s-degree graduates in six fields. Use a family confidence level of 0.99. Here qα = 4.85.Field nj x¯j sj Business 46 55.1 5.6 Communications 11 44.6 4.7
Minke Whales. In the following table are summary statistics from Exercise 16.62 on body lengths, in meters, of minke whales entangled at four different ocean depths, in meters. Use a 99% family confidence level. Here qα = 4.52.Depth nj x¯j sj 0−49 39 4.49 0.80 50−99 20 5.06 0.79 100−149 28
Denosumab and Osteoporosis. In the following table are summary statistics from Exercise 16.61 on body-mass indexes (BMI)of the women in five denosumab treatment groups. Use a family confidence level of 0.90. Here qα = 3.50.Treatment nj x¯j sj Placebo 46 25.9 4.3 14 mg 54 25.8 5.3 60 mg 47 27.5
Breast Milk and IQ. Following are summary statistics from Exercise 16.60 on IQ for samples of children at age 71/2–8 years who were born preterm. The researchers used the following designations. Group I: mothers declined to provide breast milk;Group IIa: mothers had chosen but were unable to
Artificial Teeth: Hardness. The data from Exercise 16.59 on the Vickers microhardness (VHN) of the occlusal surfaces among three different materials for making artificial teeth. Use a 95% family confidence level.In Exercises 16.106–16.109, use Procedure 16.2 on page 743 to perform a Tukey
Artificial Teeth: Wear. The data from Exercise 16.58 on the volume of material worn away, in cubic millimeters, among three different materials for making artificial teeth. Use a 95% family confidence level.
Rock Sparrows. The data from Exercise 16.57 on the number of minutes per hour that male Rock Sparrows sang in the vicinity of the nests after patch-size manipulations were done on three different groups of females. Use a 99% family confidence level.
Ground Water. The data from Exercise 16.56 on the concentrations, in milligrams per liter, of each of four chemicals among three different wells. Use a 99% family confidence level.
Monthly Rents. The data from Exercise 16.55 on monthly rents, in dollars, for independent random samples of newly completed apartments in the four U.S. regions. Use a 95% family confidence level.
Empty Stomachs. The data from Exercise 16.54 on the proportions of fish with empty stomachs among four species in African waters. Use a 99% family confidence level.
SmartPhone Battery Life. In the following table are the data from Exercise 16.53 on battery lives in hours, for samples of SmartPhones made by four different mobile companies. The four brands are iPhone 6s, iPhone 6s+, LG G3, and Samsang Galaxy S5, but we have not used the names and have permuted
Permeation Sampling. Following are the data from Exercise 16.52 on experimentally obtained calibration constants for samples of compounds in each of four compound groups.Aliphatic Aromatic Esters Alcohols hydrocarbons hydrocarbons 0.185 0.185 0.230 0.166 0.155 0.160 0.184 0.144 0.131 0.142 0.160
Theraphosaidea. Following are the data from Exercise 16.51 on Femur size of the four legs of the new genus of Theraphosaidea.Leg I Leg II Leg III Leg IV 7.72 6.74 6.44 9.16 6.38 5.39 5.82 8.37 8.59 7.36 6.92 10.0 7.36 6.22 6.72 9.69 6.93 6.98 6.01 8.71 Use a 95% family confidence level.
From Exercise 16.50: In Section 16.2, we considered two hypothetical examples to explain the logic for one-way ANOVA.a. Refer to Table 16.1 on page 724 (95% family confidence level).b. Refer to Table 16.2 on page 724 (95% family confidence level).

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Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions

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