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statistics for experimentert

Questions and Answers of Statistics For Experimentert

9.1 For this exercise, you will build a simple histogram using the SPSS sample file known as autoaccidents.sav. Open the file, select the variable named“accident” and labeled Number of accidents
8.3 You must visually display the relationship between two categorical variables using the population pyramid graphing method. The variables you use are found in the SPSS sample file called
8.2 You must summarize the data for 8,083 individuals. Specifically, you are tasked with building a 3-D pie graph showing the number and percentage of people in each of four regions. Open
8.1 You are given the task of building a pie chart that summarizes the five age categories of 582 individuals recorded in an SPSS sample file titled satisf.sav. The variable is named “agecat” and
7.3 You have a large database opened in SPSS, and now you must summarize and describe the data it contains. You decide to click Analyze on the Main Menu, then Frequencies; the Frequencies window
7.2 You need help to find out how to summarize categorical (nominal)data for a PowerPoint presentation, and you want to use a graph made from data stored in SPSS. Hint: Use the SPSS Help on the Main
7.1 How can you use the SPSS Help function to get information on transforming data in an attempt to get a more normal distribution of values?
6.3 You have been given the following scale data (test scores): 100, 109, 114, 118, 125, 135, 135, 138, 139, and 140. You must set up a database in SPSS and then transform the data using the Compute
6.2 Use the data from the variable (“avgspeed”) created in the previous exercise to recode the values into a nominal (string) variable. Your task is to use SPSS’s Recode into Different
6.1 An urban planner was tasked with recording the walking speeds (in miles per hour) of people at a downtown government center. He recorded walking speeds of the same individuals over a period of 5
5.3 The following sample data were collected by the owner of a private 640-acre forest reserve. He did a sample of 10 acres as a trial survey for the entire reserve. He needs to set up and test a
5.2 A child psychologist is investigating the behavior of children in the play area of Balboa Park. Help him set up an SPSS file to measure the following variables on individual children: time the
5.1 The highway patrol officer wants to set up an SPSS file to record traffic violations. She wishes to record data at the nominal, ordinal, and scale levels of measurement. The first item of
4.3 A political consultant wished to measure the level of politicization of the candidates for a job at the White House. He decided that the following variables would provide at least some of the
4.2 A social researcher is interested in measuring the level of religiosity of a sample of senior citizens. Help her in establishing the levels of measurement for the following variables: pray (do
4.1 The following is a list of variables that an investigator wishes to use to measure the health and survival of a particular species of earthworm:age, length, weight, moisture content, breed,
3.3 Open another one of SPSS’s sample files called customer_dbase.sav (it has 132 variables and 5,000 cases), and save it in your documents file.It’s another database that you will use several
3.2 In this exercise, you must import an Excel file from your computer and show the appearance of the Open Excel Data Source window and the first six rows of the Variable View screen. There should be
3.1 With this review exercise, you will open an SPSS sample file workprog.sav. Once it is opened, you will save it in your documents file, making it easy to access as you will need this database
2.3 You are the range safety officer at a long-distance firearms training facility.You have collected the ballistic information on four rifles—data are given below. You would like to set up a data
2.2 You must set up the SPSS Data Editor to analyze the three variables listed below on 30,000 individuals. The variables are (1) age (label is age in years, no decimals, center-aligned and scale
2.1 You have designed a data-collecting instrument that has the following five variables measured at the scale level (labels are given in parentheses;decimals are set to 3 and align to center): (1)
1.3 There was a quarter-mile drag race held at the abandoned airport last week. The makes of the winning cars were recorded by an interested fan. The results of her observations were as follows:
1.2 One day you are sitting in your professor’s office getting help on regression analysis. His phone rings; he apologizes but says that he must take the call. As you wait for him to end his phone
1.1 You have classified the size of several fish that were caught in a “catch and release” fishing contest for children as small, medium, and large.The number of fish caught by the children are
If the average of *y* depends on *x* in a non-linear way, the regression line can be quite misleading. pl875
With a controlled experiment, the slope can tell you the average change in *y* that would be caused by a change in *x*. With an observational study, however, the slope cannot be relied on to predict
How does the average of one variable depend on the values of the other variable? The regression line can be used to answer that question. pl875
In this part of the book, scatter diagrams are used to graph the associ-ation between two variables. If the scatter diagram is football-shaped, it can be summarized by the average and SD of the two
Sometimes, two quantities are thought to be connected by a linear rela-tionship (for example, length and weight in Hooke's law). The statistical problem is to estimate the slope and intercept of the
Among all lines, the regression line for y on x makes the smallest r.m.s.error in predicting y from x. For that reason, the regression line is often called the least squares line. pl875
The equation can be used to make all the regression predictions, by sub-stitution. pl875
The equation of the regression line for y on x is$$y = slope \times x + intercept$$. pl875
The intercept of the regression line equals the regression estimate for y, when x is 0. pl875
The slope of the regression line for y on x is the average change in y, per unit change in x. This equals$$r \times SD \ of \ y/SD \ of \ x$$. pl875
The regression line can be specified by two descriptive statistics: the slope and the intercept. pl875
An investigator wants to use a straight line to predict IQ from lead levels in the blood, for a representative group of children aged 5-9.14 There is a weak positive association in the data. True or
A statistician is doing a study on a group of undergraduates. On average, these students drink 4 beers a month, with an SD of 8. They eat 4 pizzas a month, with an SD of 4. There is some positive
(Continues exercise 5.) The couples in the previous exercise are followed for a year. Suppose everyone's income goes up by 10%. Find the new regression line for predicting wife's income from
A study is made of working couples. The regression equation for predicting wife's income from husband's income is wife's income = 0.1667 x husband's income + $24,000.Another investigator solves this
(a) Is the r.m.s. error of the line below around 0.1, 0.3, or 1?(b) Is it the regression line? pl875
For men age 18-24 in the HANES5 sample, the regression equation for pre-dicting height from weight is predicted height = (0.0267 inches per pound) x (weight) + 65.2 inches(Height is measured in
For women age 25-34 in the HANES5 sample, the relationship between height and income can be summarized as follows: 12 average height ≈ 64 inches, SD ≈ 2.5 inches average income ≈ $21,000, SD
Exercise 3 describes one way to predict V-SAT from M-SAT; exercise 4 describes a second way; and regression is a third way. Which way will have the smallest r.m.s.error? pl875
Repeat exercise 3, if the investigator always predicts a V-SAT of 540. pl875
A study is made of Math and Verbal SAT scores for the entering class at a certain college. The summary statistics:average M-SAT = 560, SD = 120 average V-SAT = 540, SD = 110, r = 0.66 The
For the data in table 1 (p. 209), the regression equation for predicting length from weight is predicted length = (0.05 cm per kg) x (weight) + 439.01 cm Predict the length of the wire when the
The International Rice Research Institute in the Philippines developed the hybrid rice IR 8, setting off "the green revolution" in tropical agriculture. Among other things, they made a thorough study
For the men in figure 1, the regression equation for predicting average income from education is predicted income = $2,000 per year x education + $5,000.Predict the income for one of these men who
Suppose that a scatter diagram is football-shaped. Take the points inside a narrow vertical strip. Their y-values are a new data set. The new average is estimated by the regression method. The new SD
When all the vertical strips in a scatter diagram show similar amounts of spread, the diagram is homoscedastic: the prediction errors are similar in size all along the regression line. When the
After carrying out a regression, statisticians often graph the residuals. If the residual plot shows a pattern, the regression may not have been appropriate. pl875
The SD of y is equal to the r.m.s. error of a horizontal line through the av-erage of y. The r.m.s. error of the regression line is smaller, by the factor $$√1-r^2$$.Therefore, the r.m.s. error for
The r.m.s. error of the regression line is the root-mean-square of the resid-uals. This measures the accuracy of the regression predictions. The predictions are off by amounts similar in size to the
In a scatter diagram, the vertical distance of a point above or below the regression line is the graphical counterpart of the prediction error made by the regression method. pl875
When the regression line is used to predict y from x, the difference be-tween the actual value and the predicted value is a residual, or prediction error. pl875
The bends are caused by rapid changes in air pressure, resulting in the for-mation of nitrogen bubbles in the blood. The symptoms are acute pain, and sometimes paralysis leading to death. In World
The freshmen at a large university are required to take a battery of aptitude tests. Students who score high on the mathematics test also tend to score high on the physics test. On both tests, the
In a study of high-school students, a positive correlation was found between hours spent per week doing homework, and scores on standardized achieve-ment tests. The investigators concluded that doing
Use the data in exercise 4 to answer the following questions.(a) About what percentage of students scored over 80 on the final?(b) Of the students who scored 80 on the midterm, about what percentage
A statistical analysis was made of the midterm and final scores in a large course, with the following results:average midterm score ≈ 50, SD ≈ 25 average final score ≈ 55, SD≈ 15, r≈ 0.60
Tuddenham and Snyder obtained the following results for 66 California boys at ages 6 and 18 (the scatter diagram is football-shaped):9average height at 6 ≈ 3 feet 10 inches, SD ≈ 1.7 inches,
A computer program is developed to predict the GPA of college freshmen from their high-school GPAs. This program is tried out on a class whose college GPAs are known. The r.m.s. error is 3.12. Is
The r.m.s. error of the regression line for predicting y from x is _______.(i) SD of y(ii) SD of x(iii) r x SD of y(iv) r x SD of x(v) 1-r2 x SD of y(vi) √1-r2 x SD of x
From the same study:average height of men ≈ 68 inches, SD ≈ 2.7 inches average forearm length ≈ 18 inches, SD ≈ 1 inch, r ≈ 0.80(a) What percentage of men have forearms which are 18 inches
From the same study:average height of father ≈ 68 inches, SD ≈ 2.7 inches average height of son ≈ 69 inches, SD ≈ 2.7 inches, r ≈ 0.50(a) What percentage of the sons were over 6 feet
Pearson and Lee obtained the following results for about 1,000 families:average height of husband ≈ 68 inches, SD ≈ 2.7 inches average height of wife ≈ 63 inches, SD ≈ 2.5 inches, r≈
The data in figure 9 can be summarized as follows:average education ≈ 13.0 years, SD ≈ 3.4 years average income ≈ $18,000, SD ≈ $20,000, r ≈ 0.37(a) Find the r.m.s. error of the regression
The data in figure 8 can be summarized as follows:average height of fathers ≈ 68 inches, SD ≈ 2.7 inches average height of sons ≈ 69 inches, SD≈2.7 inches, r≈ 0.5(a) Find the r.m.s. error
In 1937, the Stanford-Binet IQ test was restandardized with two forms (L and M). A large number of subjects took both tests. The results can be summarized as follows: Form L average 100, SD 15 Form M
Several regression lines are used to predict the monthly salaries in a certain com- pany, from different independent variables. Residual plots from each regression are shown below. Match the
Several different regression lines are used to predict the price of a stock (from different independent variables). Histograms for the residuals from each line are sketched below. Match the
The scatter diagram on the next page shows incomes for a sample of 168 working couples in Louisiana. Summary statistics are as follows:average husband's income = $45,000, SD = $25,000 average wife's
A regression line for predicting test scores has an r.m.s. error of 8 points.(a) About 68% of the time, the predictions will be right to within ___ points.(b) About 95% of the time, the predictions
An admissions officer is trying to choose between two methods of predicting first-year scores. One method has an r.m.s. error of 12. The other has an r.m.s. error of 7. Other things being equal,
A regression line for predicting income has an r.m.s. error of $2,000. It predicts someone's income as $20,000. This is likely to be right give or take: a few hundred dollars, a few thousand dollars,
A regression line is fitted to a small data set. For each subject, the table shows the actual value of y and the predicted value from the regression line. (The value of x is not shown.) Compute the
Look at figure 1, then say whether each statement is true or false:(a) E is above average in weight.(b) E is above average in weight, for men of his height. pl875
Look at figure 1, then fill in the blanks: person B is ______ and ______, while D is ______ and ______. Options: short, tall, skinny, chubby. pl875
Below are sketches of histograms for three lists.(a) In scrambled order, the averages are 40, 50, 60. Match the histograms with the averages.(b) Match the histogram with the description:the median is
(Hypothetical). In a clinical trial, data collection usually starts at "baseline," when the subjects are recruited into the trial but before they are randomized to treatment or control. Data
The figure below is a histogram showing the distribution of blood pressure for all 14,148 women in the Drug Study (section 5). Use the histogram to answer the following questions: (a) Is the
The figure below shows a histogram for the heights of a representative sample of men. The shaded area represents the percentage of men whose heights were between Fill in the blanks. and. P-968
In a Public Health Service study, a histogram was plotted showing the number of cigarettes per day smoked by each subject (male current smokers), as shown below. The density is marked in parentheses.
Three people plot histograms for the weights of subjects in a study, using the den- sity scale. Only one is right. Which one, and why? P-968 100 (i) 150 200 8- % per lb (i) E 100 150 200 Weight (lbs)
A histogram of monthly wages for part-time employees is shown below (densities are marked in parentheses). Nobody earned more than $1,000 a month. The block over the class interval from $200 to $500
28. Let A, B, and AB be symmetric n x n matrices aod let A and B be positive definite.Show that
27. Let A and B be n x n symmetric matrices such that ||I - xA|| ||I - yB|| =||I - xA|| ||I - yB|| for all x and y such that |x|
26. If A and B are n x n positive definite matrices and A = CC', show that∫...∫ e^(-x'C'BCx) dx₁...dxₙ = π^(n/2)|AB|^(-1/2).
25. In Prob. 23 show that the value of the integral is π^(n/2)|A + θB|^(-1/2) for all |θ| < θ₀.
24. In Prob. 23 find θ₀ as a function of the characteristic roots of A and B.
23. If A is an n x n positive definite matrix and B is a symmetric matrix, show that the integral∫...∫ e^(-x'Ax + x'Bx) dx₁...dxₙexists for all θ such that |θ| < θ₀, for a suitable
22. If x,a, and b are n x 1 vectors and A and B are n x n matrices such that A + B is nonsingular, show that(x - a)'A(x -a) + (x - b)'B(x - b)= (x - c)'(A + B)'(x -c) + (a - b)'A(A + B)'B'(a - b),
21. Let the n x 1 random vector x have a normal density given by Eq. (10.6.2) and let A be a symmetric n x n matrix of constants. Find the set of numbers (values of λ) such that the following
20. Let R be a positive definite n x n matrix and A be a symmetric n x n matrix.Show that, for some positive value of the real number λ, the matrix B is a positive definite matrix, where B = R - λA.
19. In Prob. 18 show that ????(yz) = 0 if and only if a'b = 0.
18. In Prob. 17 let the two scalar random variables y and z be defined by y = a'x, z = b'x, where a and b are vectors of constants. Find ????(y), ????(z), ????(yz).
17. Let the n x Irandom vector x have a normal density given by Eq. (10.6.2) with JI=0 and V = I. Find the matrix C, where C = 8(xx').
16. Let the n x 1 random vector x have a normal density with mean vector equal to zero and with covariance matrix I; that is, by Eq. (10.6.2) the density is denoted by N(x; 0, I). Show that
15. Let the n x 1 random vector x have a normal density with mean vector equal to μand covariance matrix equal to D, where D is a diagonal matrix. Show that$$8[(x - \mu)'A(x - \mu)] = \sum_{i=1}^{n}

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