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statistics for experimentert

Statistics 4th Edition David Freedman, Robert Pisani, Roger Purves - Solutions

In a large statistics class, the correlation between midterm scores and fi- nal scores is found to be nearly 0.50, every term. The scatter diagrams are football-shaped. Predict the percentile rank on the final for a student whose percentile rank on the midterm is (a) 5% (b) 80% (c) 50% (d) unknown
A large study was made on the blood-pressure problem discussed in the pre-vious exercise. It found that first readings average 130 mm, and second read-ings average 120 mm; both SDs were about 15 mm. Does this support either doctor's argument? Or is it the regression effect? Explain. PL968
A doctor is in the habit of measuring blood pressures twice. She notices that patients who are unusually high on the first reading tend to have somewhat lower second readings. She concludes that patients are more relaxed on the second reading. A colleague disagrees, pointing out that the patients
Three lines are drawn across the scatter diagram below. One is the SD line, one is the regression line for y on x, and one is the regression line for x on y. Which is which? Why? (The "regression line for y on x" is used to predict y from x.) PL968
An investigator measuring various characteristics of a large group of athletes found that the correlation between the weight of an athlete and the amount of weight that athlete could lift was 0.60. True or false, and explain:(a) On the average, an athlete can lift 60% of his body weight.(b) If an
In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50; both averaged 12 years of schooling completed, with an SD of 3 years. PL968 7?
Pearson and Lee obtained the following results in a study of 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 ≈ 0.25 Predict the height of a wife when the height of her husband is(a) 72 inches (b) 64 inches
In a study of the stability of IQ scores, a large group of individuals is tested once at age 18 and again at age 35. The following results are obtained.age 18: average score ≈ 100, SD ≈ 15 age 35: average score ≈ 100, SD ≈ 15, r ≈ 0.80(a) Estimate the average score at age 35 for all the
In example 2 (p. 166), the regression method predicted that a student at the 90th percentile on the SAT would only be at the 69th percentile on first-year GPA. True or false, and explain: a student at the 69th percentile on first-year GPA should be at the 90th percentile on the SAT. PL968
In Pearson's study, the sons of the 72-inch fathers only averaged 71 inches in height. True or false: if you take the 71-inch sons, their fathers will average about 72 inches in height. Explain briefly. PL968
For the men age 18-24 in the HANES5 sample, the ones who were 63 inches tall averaged 138 pounds in weight. True or false, and explain: the ones who weighed 138 pounds must have averaged 63 inches in height. PL968
In the data set of figures 5 and 6, are the sons of the 61-inch fathers taller on the average than the sons of the 62-inch fathers, or shorter? What is the explanation? PL968
An instructor standardizes her midterm and final each semester so the class average is 50 and the SD is 10 on both tests. The correlation between the tests is around 0.50. One semester, she took all the students who scored below 30 at the midterm, and gave them special tutoring. They all scored
As part of their training, air force pilots make two practice landings with instruc-tors, and are rated on performance. The instructors discuss the ratings with the pilots after each landing. Statistical analysis shows that pilots who make poor land-ings the first time tend to do better the second
For the first-year students at a certain university, the correlation between SAT scores and first-year GPA was 0.60. The scatter diagram is football-shaped. Predict the percentile rank on the first-year GPA for a student whose percentile rank on the SAT was(a) 90% (b) 30%(c) 50% (d) unknown Compare
In a certain class, midterm scores average out to 60 with an SD of 15, as do scores on the final. The correlation between midterm scores and final scores is about 0.50.The scatter diagram is football-shaped. Predict the final score for a student whose midterm score is(a) 75 (b) 30(c) 60(d) unknown
Suppose *r* = -1. Can you explain why a one-SD increase in *x* is matched by a one-SD decrease in *y*?The answers to these exercises are on pp. A59-60. PL968
For women age 25-34 in the U.S. in 2005, with full-time jobs, the relationship between education (years of schooling completed) and personal income can be summarized as follows:2 average education≈ 14 years, SD ≈ 2.4 years average income ≈ $32,000, SD ≈ $26,000, *r* ≈ 0.34 Estimate the
The men age 45-74 in HANESS had an average height of 69 inches, equal to the overall average height (exercise 2). True or false, and explain: their average weight should be around 190 pounds, that being the overall average weight. PL968
For the men age 18 and over in HANESS, average height ≈ 69 inches, SD ≈ 3 inches average weight ≈ 190 pounds, SD≈ 42 pounds, *r* ≈ 0.41 Estimate the average weight of the men whose heights were(a) 69 inches (b) 66 inches (c) 24 inches (d) 0 inches Comment on your answers to (c) and (d).
In a certain class, midterm scores average out to 60 with an SD of 15, as do scores on the final. The correlation between midterm scores and final scores is about 0.50.Estimate the average final score for the students whose midterm scores were(a) 75(b) 30 (c) 60 Plot your regression estimates, as
Shown below is a scatter diagram for educational levels (years of schooling completed) of husbands and wives in South Carolina, from the March 2005 Current Population Survey.(a) The points make vertical and horizontal stripes. Why? PL968
As part of the study described in exercise 10, the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state. (Again, D.C. counts as a state.) The corre-lation between these 51 pairs of averages was 0.97. Would the
In a study of 2005 Math SAT scores, the Educational Testing Service com-puted the average score for each of the 51 states, and the percentage of the high-school seniors in that state who took the test. 14 (For these purposes, D.C.counts as a state.) The correlation between these two variables was
At the University of California, Berkeley, Statistics 2 is a large lecture course with small discussion sections led by teaching assistants. As part of a study, at the second-to-last lecture one term, the students were asked to fill out anony-mous questionnaires rating the effectiveness of their
For women age 25 and over in the U.S. in 2005, the relationship between age and educational level (years of schooling completed) can be summarized as follows:12 average age ≈ 50 years, SD ≈ 16 years average ed. level ≈ 13.2 years, SD≈ 3.0 years, r≈-0.20 True or false, and explain: as you
A number is missing in each of the data sets below. If possible, fill in the blank to make *r* equal to 1. If this is not possible, say why not. PL968
An investigator collected data on heights and weights of college students;results can be summarized as follows.Average SD Men's height 70 inches 3 inches Men's weight 144 pounds 21 pounds Women's height 64 inches 3 inches Women's weight 120 pounds 21 pounds The correlation coefficient between
In each case, say which correlation is higher, and explain briefly. (Data are from a longitudinal study of growth.)(a) Height at age 4 and height at age 18, height at age 16 and height at age 18.(b) Height at age 4 and height at age 18, weight at age 4 and weight at age 18.(c) Height and weight at
True or false, and explain briefly:(a) If the correlation coefficient is -0.80, below-average values of the dependent variable are associated with below-average values of the independent variable.(b) If y is usually less than x, the correlation coefficient between x and y will be negative. PL968
When studying one variable, you can use a graph called a _______. When studying the relationship between two variables, you can use a graph called a _______. PL968
Many economists believe that there is trade-off between unemployment and infla-tion: low rates of unemployment will cause high rates of inflation, while higher rates of unemployment will reduce the rate of inflation. The relationship between the two variables is shown below for the U.S. in the
Many studies have found an association between cigarette smoking and heart dis-ease. One study found an association between coffee drinking and heart disease. 10 Should you conclude that coffee drinking causes heart disease? Or can you explain the association between coffee drinking and heart
Studies find a negative correlation between hours spent watching television and scores on reading tests. Does watching television make people less able to read?Discuss briefly. PL968
The correlation between height and weight among men age 18-74 in the U.S. is about 0.40. Say whether each conclusion below follows from the data; explain your answer. (a) Taller men tend to be heavier. (b) The correlation between weight and height for men age 18-74 is about 0.40. (c) Heavier men
Is the correlation in figure 8 ecological? How is that relevant to the argument? PL968
The scatter diagram in figure 7 shows stripes. Why? PL968
A sociologist is studying the relationship between suicide and literacy in nineteenth-century Italy. He has data for each province, showing the percentage of literates and the suicide rate in that province. The correlation is 0.6. Does this give a fair estimate of the strength of the association
The table at the top of the next page is adapted from Doll and shows per capita consumption of cigarettes in various countries in 1930, and the death rates from lung cancer for men in 1950. (In 1930, hardly any women smoked; and a long period of time is needed for the effects of smoking to show
The National Health and Nutrition Examination Survey (p. 58) also covers children. In HANES2, at each age from 6 to 11, the correlation between height and weight was just about 0.67. For all the children together, would the correlation between height and weight be just about 0.67, somewhat more
In the figure below, 6 scatter diagrams are plotted on the same pair of axes; in the first, the points are marked "a"; in the second, "b"; and so forth. For each of the 6 diagrams taken on its own, the correlation is around 0.6. Now take all the points together. For the combined diagram, is the
Six data sets are shown below. In (i), the correlation is 0.8571, and in (ii) the correlation is 0.7857. Find the correlations for the remaining data sets. No arithmetic is necessary.(i)(ii)(iii)(iv)(v)(vi)x yx yx yx yx yx y1 21 22 12 21 40 62 32 33 23 32 61 93 13 11 34 13 22 34 44 45 44 83 12 56
Two weathermen compute the correlation between daily maximum temperatures for Washington and Boston. One does it for June; the other does it for the whole year. Who gets the bigger correlation? ("Washington" is the city, not the state.) PL968
In figure 1 on p. 120, the correlation is 0.5. Suppose we plot on the horizontal axis the height of the paternal grandfather (not the father); the height of the son is still plotted on the vertical axis. Would the correlation be more or less than 0.5? PL968
Two different investigators are working on a growth study. The first measures the heights of 100 children, in inches. The second prefers the metric system, and changes the results to centimeters (multiplying by the conversion factor 2.54 centimeters per inch). A scatter diagram is plotted, showing
Suppose the correlation between x and y is 0.73.(a) Does the scatter diagram slope up or down?(b) If you multiply all the values of y by -1, would the new scatter diagram slope up or down?(c) If you multiply all the values of y by -1, what happens to the correlation? PL968
As in exercise 2, but you interchange the last two values (5 and 6) for y. PL968
As in exercise 2, but you double each value of x. PL968
As in exercise 2, but you add 3 to each value of y instead of interchanging the columns. PL968
A small data set is shown below; r≈ 0.76. If you switch the two columns, does this changer? Explain or calculate.x y 1 2 2 3 3 1 4 5 5 6
(a) In June 2005, which city was warmer—Boston or New York? Or were they about the same?(b) In the left hand panel of figure 2, all the dots are above the 45-degree line.Why? PL968
On the Math SAT, men have a distinct edge. In 2005, for instance, the men averaged about 538, and the women averaged about 504.(a) Estimate the percentage of men getting over 700 on this test in 2005.(b) Estimate the percentage of women getting over 700 on this test in 2005.You may assume (i) the
From the mid-1960s to the early 1990s, there was a slow but steady decline in SAT scores. For example, take the Verbal SAT. The average in 1967 was about 543; by 1994, the average was down to about 499. However, the SD stayed close to 110. The drop in averages has a large effect on the tails of the
You are looking at a computer printout of 100 test scores, which have been converted to standard units. The first 10 entries are-6.2 3.5 1.2 -0.13 4.3 -5.1 -7.2 -11.3 1.8 6.3 Does the printout look reasonable, or is something wrong with the computer? p-968
The following list of test scores has an average of 50 and an SD of 10:39 41 47 58 65 37 37 49 56 59 62 36 48 52 64 29 44 47 49 52 53 54 72 50 50(a) Use the normal approximation to estimate the number of scores within 1.25 SDs of the average.(b) How many scores really were within 1.25 SDs of the
In figure 2 (p. 81), the percentage of women with heights between 61 inches and 66 inches is exactly equal to the area between 61 inches and 66 inches under the **normal**and approximately equal to the area under the **curve, histogram**.The answers to these exercises are on pp. A51-52. p-968
In a law school class, the entering students averaged about 160 on the LSAT; the SD was about 8. The histogram of LSAT scores followed the normal curve reasonably well. (LSAT scores range from 120 to 180; among all test-takers, the average is around 150 and the SD is around 9.)(a) About what
THE NORMAL CURVE The normal curve was discovered around 1720 by Abraham de Moivre, while he was developing the mathematics of chance. (His work will be discussed again in parts IV and V.) Around 1870, the Belgian mathematician Adolph Quetelet had the idea of using the curve as an ideal histogram,
In HANES5, the men age 18 and over had an average height of 69 inches and an SD of 3 inches. The histogram is shown below, with a normal curve.The percentage of men with heights between 66 inches and 72 inches is ex-actly equal to the area between (a) and (b) under the (c)percentage is
Among applicants to one law school, the average LSAT score was about 169, the SD was about 9, and the highest score was 178. Did the LSAT scores follow the normal curve? p-968
Among freshmen at a certain university, scores on the Math SAT followed the normal curve, with an average of 550 and an SD of 100. Fill in the blanks;explain briefly.(a) A student who scored 400 on the Math SAT was at the ___th per-centile of the score distribution.(b) To be at the 75th percentile
One term, about 700 Statistics 2 students at the University of California, Berkeley, were asked how many college mathematics courses they had taken, other than Statistics 2. The average number of courses was about 1.1; the SD was about 1.5. Would the histogram for the data look like (i), (ii), or
For women age 25-34 with full time jobs, the average income in 2004 was$32,000. The SD was $26,000, and 1/4 of 1% had incomes above $150,000.Was the percentage with incomes in the range from $32,000 to $150,000 about 40%, 50%, or 60%? Choose one option and explain briefly.5 p-968
Which of the following are true? false? Explain or give examples.(a) The median and the average of any list are always close together.(b) Half of a list is always below average.(c) With a large, representative sample, the histogram is bound to follow the normal curve quite closely.(d) If two lists
True or false, and explain briefly—(a) If you add 7 to each entry on a list, that adds 7 to the average.(b) If you add 7 to each entry on a list, that adds 7 to the SD.(c) If you double each entry on a list, that doubles the average.(d) If you double each entry on a list, that doubles the SD.(e)
The figure below has six scatter diagrams for hypothetical data. The correla- tion coefficients, in scrambled order, are: -0.85 -0.38 -1.00 0.06 0.97 0.62 P-698
In one class, the correlation between scores on the final and the midterm was 0.50, while the correlation between the scores on the final and the homework was 0.25. True or false, and explain: the relationship between the final scores and the midterm scores is twice as linear as the relationship
Three data sets are collected, and the correlation coefficient is computed in each case. The variables are(i) grade point average in freshman year and in sophomore year(ii) grade point average in freshman year and in senior year(iii) length and weight of two-by-four boards Possible values for
Is the correlation between the heights of husbands and wives in the U.S.around -0.9, -0.3, 0.3, or 0.9? Explain briefly. P-698
Suppose men always married women who were exactly 8% shorter. What would the correlation between their heights be? P-698
(a) For a representative sample of cars, would the correlation between the age of the car and its gasoline economy (miles per gallon) be positive or negative?(b) The correlation between gasoline economy and income of owner turns out to be positive. How do you account for this positive association?
Using the same data as in exercise 3, say whether each of the following students was on the SD line:(a) height 75 inches, weight 180 pounds(b) height 66 inches, weight 130 pounds(c) height 66 inches, weight 120 pounds The answers to these exercises are on p. A57. P-698
One study on male college students found their average height to be 69 inches, with an SD of 3 inches. Their average weight was 140 pounds, with an SD of 20 pounds. And the correlation was 0.60. If one of these people is 72 inches tall, how heavy would he have to be to fall on the SD line? P-698
For the scatter diagram shown below, say whether it is the solid line or the dashed line which is the SD line. P-698 yx
True or false:(a) The SD line always goes through the point of averages.(b) The SD line always goes through the point (0, 0). P-698
Investigators take a sample of DINKS (dual-income families-where husband and wife both work-and no kids). The investigators have data on the husband's in-come and the wife's income. By definition, family income = husband's income + wife's income.The average family income was around $85,000, and 10%
Investigators are studying registered students at the University of California. The students fill out questionnaires giving their year of birth, age (in years), age of mother, and so forth. Fill in the blanks, using the options given below, and explain briefly.(a) The correlation between student's
(a) If women always married men who were five years older, the correlation be-tween the ages of husbands and wives would be ______. Choose one of the options below, and explain.(b) The correlation between the ages of husbands and wives in the U.S. is ______.Choose one option, and explain.exactly -1
In figure 1, if you took only the fathers who were taller than 6 feet, and their sons, would the correlation between the heights be around -0.3, 0, 0.5 or 0.8? P-698
In figure 1, is the correlation between the heights of the fathers and sons around-0.3, 0, 0.5, or 0.8? P-698
For each scatter diagram below:(a) The average of x is around 1.0 1.5 2.0 2.5 3.0 3.5 4.0(b) Same, for y.(c) The SD of x is around 0.25 0.5 1.0 1.5(d) Same, for y.(e) Is the correlation positive, negative, or 0? P-698
(a) Would the correlation between the age of a second-hand car and its price be positive or negative? Why? (Antiques are not included.)(b) What about the correlation between weight and miles per gallon? P-698
The scatter diagram below shows scores on the midterm and final in a certain course.(a) Was the average midterm score around 25, 50, or 75?(b) Was the SD of the midterm scores around 5, 10, or 20?(c) Was the SD of the final scores around 5, 10, or 20?(d) Which exam was harder-the midterm or the
Students named A, B, C, D, E, F, G, H, I, and J took a midterm and a final in a certain course. A scatter diagram for the scores is shown on the next page.(a) Which students scored the same on the midterm as on the final?(b) Which students scored higher on the final? P-698
Draw the scatter diagram for each of the following hypothetical data sets. The variable labeled "x" should be plotted along the x-axis, the one labeled "y" along the y-axis. Mark each axis fully. In some cases, you will have to plot the same point more than once. The number of times such a multiple
Below is a scatter diagram for some hypothetical data.(a) Is the average of the x-values around 1, 1.5, or 2?(b) Is the SD of the x-values around 0.1, 0.5, or 1?(c) Is the average of the y-values around 1, 1.5, or 2?(d) Is the SD of the y-values around 0.5, 1.5, or 3? P-698
Below is the scatter diagram for a certain data set. Fill in the blanks. P-698
Use figure 1 (p. 120) to answer the following questions:(a) What is the height of the shortest father? of his son?(b) What is the height of tallest father? of his son?(c) Take the families where the father was 72 inches tall, to the nearest inch.How tall was the tallest son? the shortest son?(d)
True or false:(b) (1.5, 2.5) (c) (2.5, 1.5)(a) If y is bigger than x, then the point (x, y) is above the line of exercise 4.(b) If y = x, then the point (x, y) is on the line of exercise 4.(c) If y is smaller than x, then the point (x, y) is below the line of exercise 4. P-698
For each of the following points, say whether it is on the line of exercise 4, or above, or below: P-698(a) (0, 0)
Plot the points (1, 1), (2, 2), (3, 3), and (4, 4) on the same graph. These points all lie on a line. What is the equation of this line? P-698
Plot four different points whose y-coordinates are double their x-coordinates. Do these points lie on a line? If so, what is the equation of the line? P-698
Figure 25 shows three lines. Match the lines with the equations:y = 3/4x + 1 y = -1/2x + 4 y = -1/2x + 2 P-698
Plot the graphs of the following equations:(a) y = 2x + 1 (b) y = 1/2x + 2 In each case, say what the slope and intercept are, and give the height of the line at x = 2. P-698
Draw the line with intercept 2 and slope 1.The answers to these exercises are on p. A54. P-698
Draw the line with intercept 2 and slope -1. Hint: this line goes through the point (0, 2). P-698
The same but move over 6 and up 5. P-698
The same, but move over 4 and up 2. P-698
Start at the point (2, 1) in figure 21. If you move over 2 and up 1, will you be on the line, above the line, or below the line? P-698
Draw lines through the point (2, 1) with the following slopes: P-698(a) +1 (b) -1(c) 0

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