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statistics for experimentert

Questions and Answers of Statistics For Experimentert

35. Find det (A x B) and det (B x A) if$$A = \begin{bmatrix} 2 & 1 \\ 3 & 4 \\ \end{bmatrix} B = \begin{bmatrix} 1 & 0 & 2 \\ 2 & 1 & 3 \\ 2 & 4 & 1 \\ \end{bmatrix}$$
34. In Prob. 33 demonstrate that A x B = (A x I)(I x B).
33. Compute A x B and B x A for the matrices below.$$A = [1, -1, 0]; B = \begin{bmatrix} 3 & 1 \\ 4 & 2 \\ 2 & 0 \\ \end{bmatrix}$$
32. If A and B are symmetric matrices, show that A x B is symmetric.
31. Use the details of the proof of Theorem 8.6.1 to find a lower triangular matrix R and an upper triangular matrix T such that A = RT where$$A = \begin{bmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 &
30. Generalize Prob. 29; that is, find the inverse of the matrix T, where T is a *k* x *k* lower triangular matrix, where each element on and below the main diagonal is equal to unity.
29. Find the inverse of the 5 x 5 lower triangular matrix T where$$T = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 \\
28. Work Probs. 26 and 27 when A is a k x k matrix.
27. Find the inverse of A in Prob. 26 assuming conditions on the 0i andb, such that the inverse exists.
26. Find the determinant of the matrix$$A =\begin{bmatrix}0 & a_1 & 0 & 0\\b_1 & 0 & a_2 & 0\\0 & b_2 & 0 & a_3\\0 & 0 & b_3 & 0\end{bmatrix}$$
25. Let the 2*k* x 2*k* matrix A be partitioned as follows$$A=\begin{bmatrix}A_{11} & A_{12}\\A_{21} & A_{22}\end{bmatrix}$$where *A11* is a *k* x *k* matrix; further suppose that *A21A22* = *A22A21*
24. Evaluate the determinant of A where *xi* = *i* and *k* = 4.$$A =\begin{bmatrix}1 & 1 & 1 & \cdots & 1 \\x_1 & x_2 & x_3 & \cdots & x_k \\x_1^2 & x_2^2 & x_3^2 & \cdots & x_k^2 \\\vdots & \vdots &
23. Use Theorem 8.2.1, to find the determinant of the matrix A where A =$$\begin{bmatrix}1 & 3 & 1 & 3 \\4 & 2 & 2 & 1 \\4 & 2 & 2 & 3 \\3 & 1 & 4 & 1\end{bmatrix}$$
22. Evaluate the determinant of the matrix B where B is defined by
21. Use Theorem 8.4.3 to evaluate the determinant of the matrix V in Example 8.3.3
20. Use Theorem 8.9.3 to find the characteristic roots of the matrix in Prob. 19.
19. Use Theorem 8.9.3 to find the determinant of B where$$B = \begin{bmatrix} 2 & 2 & 3 \\ 2 & 5 & 6 \\ 3 & 6 & 10 \end{bmatrix}$$.Note that B = I + bb' where b' = [1, 2, 3].
18. Prove Theorem 8.9.5 by using Theorem 8.2.1.
17. Use Theorem 8.2.1 to find the inverse of A where$$A = \begin{bmatrix} 1 & 0 & 0 & 0 & 3 \\ 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 2 \\ 3 & 2 & 1 & 2 & 4 \end{bmatrix}$$
16. Find A-1 in Prob. 14.
15. Find the inverse of the matrix in Prob. 3.
14. Find the determinant and characteristic roots of the matrix A where$$A = \begin{bmatrix} 0 & 1 & 1 & ... & 1 \\ 1 & 0 & 1 & ... & 1 \\ 1 & 1 & 0 & ... & 1 \\ . & . & . & ... & . \\ 1 & 1 & 1 &
13. Extend Prob. 12to the case in which there are 712 block matrices and the order of each is k x k.
12. Find the inverse of the triangular matrix T where [I J J T=0 I 0 0
11. If 6 6 6 6 6 6 8 8 8 8 B=6 8 3 3 3 6 8 3 2 2 6 8 3 2 4 find B.
10. Generalize Probs. 8 and 9 to a k x k matrix.
9. If the conditions on thea, in the matrix A in Prob. 8 are such that A is nonsingular, find A.
8. Let a a a a az az az A= a az az az a az az a what are the conditions on thea, so that A is nonsingular?
7. Find the determinant of the matrix. Tal J J J al J J C = J Jal J Jal JJ where a 0 and each matrix has dimension n x n. What are the conditions on a and n to insure that the inverse exists?
6. Find the inverse of the matrix C where$$C =\begin{bmatrix}a₁ & a₂ & a₂ & a₂ \\a₂ & a₃ & a₄ & a₄ \\a₂ & a₄ & a₃ & a₄ \\a₂ & a₄ & a₄ & a₃\end{bmatrix}$$if the ai are
5. In Theorem 8.2.1, suppose n₁ = n₂ and B₁₁ = B₂₂ = 0. State a result for the existence of B-¹.
4. Let a k x k matrix C be defined by Eq. (8.3.13).(a) Find the conditions on the constantsa, b, and k such that C is positive definite.(b) Find the conditions on the constantsa, b, and k such that C
3. If B = $$\begin{bmatrix}-I & A-I \\A-I & A\end{bmatrix}$$, where A is an m x m symmetric matrix such that A² = A, show that |B| = (-1)m.
2. In Prob. 1, if ad - b² ≠ 0, find B-¹.
1. If B = $$\begin{bmatrix}a I & bI \\bI & dI\end{bmatrix}$$, where each identity matrix is of size m x m, find the character-istic roots of B.
If a study draws conclusions about the effects of age, find out whether the data are cross-sectional or longitudinal. p-968
Roughly 68% of the entries on a list of numbers are within one SD of the average, and about 95% are within two SDs of the average. This is so for many lists, but not all. p-968
The SD measures distance from the average. Each number on a list is off the average by some amount. The SD is a sort of average size for these amounts off. More technically, the SD is the r.m.s. size
r.m.s. size of a list average of (entries). p-968
The r.m.s. size of a list measures how big the entries are, neglecting signs. p-968
Half the area under a histogram lies to the left of the median, and half to the right. The median is another way to locate the center of a histogram. p-968
The average locates the center of a histogram, in the sense that the his- togram balances when supported at the average. p-968
Average of a list = sum of entries number of entries? p-968
A typical list of numbers can be summarized by its average and standard deviation (SD). p-968
Many observers think there is a permanent underclass in American society—most of those in poverty typically remain poor from year to year. Over the pe-riod 1970-2000, the percentage of the American
As in exercise 10, but a whole series of students are chosen. The r.m.s. size of your losses should be around _____ Fill in the blank. p-968
Incoming students at a certain law school have an average LSAT (Law School Aptitude Test) score of 163 and an SD of 8. Tomorrow, one of these students? p-968
An investigator has a computer file showing family incomes for 1,000 sub-jects in a certain study. These range from $5,800 a year to $98,600 a year. By accident, the highest income in the file gets
In the HANES5 sample, the average height of the boys was 137 cm at age 9 and 151 cm at age 11. At age 11, the average height of all the children was 151 cm. 14(a) On the average, are boys taller than
A study on college students found that the men had an average weight of about 66 kg and an SD of about 9 kg. The women had an average weight of about 55 kg and an SD of 9 kg.(a) Find the averages and
For the men age 18-24 in HANESS, the average systolic blood pressure was 116 mm and the SD was 11 mm. 13 Say whether each of the following blood pressures is unusually high, unusually low, or about
For persons age 25 and over in the U.S., would the average or the median be higher for income? for years of schooling completed?--- OCR End --- p-968
Here is a list of numbers:0.7 1.6 9.8 3.2 5.4 0.8 7.7 6.3 2.2 4.1 8.1 6.5 3.7 0.6 6.9 9.9 8.8 3.1 5.7 9.1(a) Without doing any arithmetic, guess whether the average is around 1, 5, or 10.(b) Without
(a) Both of the following lists have the same average of 50. Which one has the smaller SD, and why? No computations are necessary. p-968(i) 50, 40, 60, 30, 70, 25, 75(ii) 50, 40, 60, 30, 70, 25, 75,
(a) Find the average and SD of the list 41, 48, 50, 50, 54, 57.(b) Which numbers on the list are within 0.5 SDs of average? within 1.5 SDs of average? p-968
For a list of positive numbers, can the SD ever be larger than the average?The answers to these exercises are on pp. A50-51. p-968
Can the SD ever be negative? p-968
For the list 107, 98, 93, 101, 104, which is smaller—the r.m.s. size or the SD? No arithmetic is needed. p-968
What is the r.m.s. size of the list 17, 17, 17, 17, 17? the SD? p-968
(a) The Governor of California proposes to give all state employees a flat raise of $250 a month. What would this do to the average monthly salary of state employees? to the SD?(b) What would a 5%
Repeat exercise 5 for the following two lists: p-968(i) 5, -4, 3, -1, 7(ii) -5, 4, -3, 1, -7
(a) For each list below, work out the average, the deviations from average, and the SD.(i) 1, 3, 4, 5, 7(ii) 6, 8, 9, 10, 12(b) How is list (ii) related to list (i)? How does this relationship carry
Three instructors are comparing scores on their finals; each had 99 students. In class A, one student got 1 point, another got 99 points, and the rest got 50 points.In class B, 49 students got a
Someone is telling you how to calculate the SD of the list 1, 2, 3, 4, 5:The average is 3, so the deviations from average are-2 -1 0 1 2 The 0 doesn't count, so the r.m.s. deviation
Someone is telling you how to calculate the SD of the list 1, 2, 3, 4, 5:The average is 3, so the deviations from average are-2 -1 0 1 2 Drop the signs. The average deviation is$$
Guess which of the following two lists has the larger SD. Check your guess by computing the SD for both lists. p-968(i) 9, 9, 10, 10, 10, 12(ii) 7, 8, 10, 11, 11, 13
As in exercise 9, but tomorrow a whole series of men will be chosen at random.After each man appears, his actual height will be compared with your guess to see how far off you were. The r.m.s. size
The men in the HANESS sample had an average height of 69 inches, and the SD was 3 inches. Tomorrow, one of these men will be chosen at random. You have to guess his height. What should you guess? You
One investigator takes a sample of 100 men age 18-24 in a certain town. Another takes a sample of 1,000 such men.(a) Which investigator will get a bigger average for the heights of the men in his
Below are sketches of histograms for three lists. Match the sketch with the de-scription. Some descriptions will be left over. Give your reasoning in each case. p-968(i) ave ≈ 3.5, SD ≈ 1(ii) ave
The SD for the ages of the people in the HANES5 sample is around $$ \underline{ } $$. Fill in the blank, using one of the options below. Explain briefly. (This survey was discussed in section 2; the
Each of the following lists has an average of 50. For each one, guess whether the SD is around 1, 2, or 10. (This does not require any arithmetic.) p-968(a) 49, 51, 49, 51, 49, 51, 49, 51, 49, 51(b)
Each of the following lists has an average of 50. For which one is the spread of the numbers around the average biggest? smallest? p-968(i) 0, 20, 40, 50, 60, 80, 100(ii) 0, 48, 49, 50, 51, 52,
This continues exercise 1.(a) Here are the heights of four boys: 150 cm, 130 cm, 165 cm, 140 cm. Match the heights with the descriptions. A description may be used twice.unusually short about average
The Public Health Service found that for boys age 11 in HANES2, the average height was 146 cm and the SD was 8 cm. Fill in the blanks.(a) One boy was 170 cm tall. He was above average, by $$
A computer is programmed to predict test scores, compare them with actual scores, and find the r.m.s. size of the prediction errors. Glancing at the printout, you see the r.m.s. size of the
The list 103, 96, 101, 104 has an average. Find it. Each number in the list is off the average by some amount. Find the r.m.s. size of the amounts off. p-968
Each of the numbers 103, 96, 101, 104 is almost 100 but is off by some amount.Find the r.m.s. size of the amounts off. p-968
(a) Find the r.m.s. size of the list 7, 7, 7, 7.(b) Repeat, for the list 7, -7, 7, -7. p-968
Guess whether the r.m.s. size of each of the following lists of numbers is around 1, 10, or 20. No arithmetic is required. p-968(a) 1, 5, -7, 8, -10, 9, -6, 5, 12, -17(b) 22, -18, -33, 7, 31, 12, 1,
(a) Find the average and the r.m.s. size of the numbers on the list 1, -3, 5, -6, 3.(b) Do the same for the list -11, 8, -9, -3, 15. p-968
For each of the following lists of numbers, say whether the entries are on the whole around 1, 5, or 10 in size. No arithmetic is needed. p-968(a) 1.3, 0.9, 1.2, 0.8(c) 7, 3, 6, 4(b) 13, 9, 12, 8(d)
For registered students at universities in the U.S., which is larger: average age or median age? p-968
For this cigarette histogram, is the average around 15, 20, or 25? p-968
Look back at the cigarette histogram on p. 42. The median is around ______ . Fill in the blank. Options: 10, 20, 30, 40 p-968
For each histogram in exercise 1, is the median equal to the average? or is it to the left? to the right? p-968
Below are sketches of histograms for three lists. Fill in the blank for each list: the average is around ______ . Options: 25, 40, 50, 60, 75. p-968(a)(b)(c)ANA 50 100 50 100 50 100
Average hourly earnings are computed each month by the Bureau of Labor Statis- tics using payroll data from commercial establishments. The Bureau figures the total wages paid out (to nonsupervisory
Diastolic blood pressure is considered a better indicator of heart trouble than sys-tolic pressure. The figure below shows age-specific average diastolic blood pres-sure for the men age 20 and over
In figure 2, are the Rocky Mountains plotted near the left end of the axis, the middle, or the right end? What about Kansas? What about the trenches in the sea floor, like the Marianas trench? p-968
Twenty-one people in a room have an average height of 5 feet 6 inches. A 22nd person enters the room. How tall would he have to be to raise the average height by 1 inch? p-968
Twenty-one people in a room have an average height of 5 feet 6 inches. A 22nd person, who is 6 feet 5 inches tall, enters the room. Find the average height of all 22 people. Compare with exercise 4.
Ten people in a room have an average height of 5 feet 6 inches. An 11th person, who is 6 feet 5 inches tall, enters the room. Find the average height of all 11 people. p-968
Which of the following two lists has a bigger average? Or are they the same? Try to answer without doing any arithmetic. p-968(i) 10, 7, 8, 3, 5, 9 (ii) 10, 7, 8, 3, 5, 9, 11
A list has 10 entries. Each entry is either 1 or 2 or 3. What must the list be if the average is 1? If the average is 3? Can the average be 4? p-968
(a) The numbers 3 and 5 are marked by crosses on the horizontal line below. Find the average of these two numbers and mark it by an arrow.*3 5(b) Repeat (a) for the list 3, 5, 5.X 3*5(c) Two numbers
12.31 Can people tell the difference between a female nose and a male nose? This important (?) research question was examined in the article “You Can Tell by the Nose: Judging Sex from an Isolated
12.30 A story describing a date rape was read by 352 high school students. To investigate the effect of the victim’s clothing on subject’s judgment of the situation described, the story was
12.29 A survey was conducted in the San Francisco Bay area in which each participating individual was classified according to the type of vehicle used most often and city of residence. A subset of
12.28 The 2006 Expedia Vacation Deprivation Survey(Ipsos Insight, May 18, 2006) described the results of a poll of working adults in Canada. Each person in a random sample was classified according to

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