Essentials Of Social Statistics For A Diverse Society 3rd Edition Anna Y Leon Guerrero, Chava Frankfort Nachmias - Solutions

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41. Use the definition in Expression (3.13) to prove that V(aXb) a2 2 X. [Hint: With h(X) aXb, E[h(X)] a b where E(X).]
14. The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants” (Water Research, 1984: 1169–1174) suggests the uniform distribution on the interval (7.5, 20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.
13. Example 4.5 introduced the concept of time headway in traffic flow and proposed a particular distribution for X the headway between two randomly selected consecutive cars (sec). Suppose that in a different traffic environment, the distribution of time headway has the form f(x) k x4 x 1 0 x
12. The cdf for X ( measurement error) of Exercise 3 is 0 x 2 F(x) 1 2 3 32 4x x 33 2 x 2 1 2 xa. Compute P(X 0).b. Compute P(1 X 1).c. Compute P(.5 X).d. Verify that f(x) is as given in Exercise 3 by obtaining F (x).e. Verify that 0.
10. A family of pdf’s that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and , both 0, and the pdf is f(x; k, ) k xk1 k x 0 x a. Sketch the graph of f(x; k, ).b. Verify that the total
9. Consider again the pdf of X time headway given in Example 4.5. What is the probability that time headway isa. At most 6 sec?b. More than 6 sec? At least 6 sec?c. Between 5 and 6 sec?
8. In commuting to work, I must first get on a bus near my house and then transfer to a second bus. If the waiting time(in minutes) at each stop has a uniform distribution with A 0 and B 5, then it can be shown that my total waiting time Y has the pdfa. Sketch a graph of the pdf of Y.b. Verify
7. The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A 25 and B 35.a. Determine the pdf of X and sketch the corresponding density curve.b. What is the probability that preparation time exceeds 33 min?c. What is
42. Suppose E(X) 5 and E[X(X 1)] 27.5. What isa. E(X2)? [Hint: E[X(X 1)] E[X2 X] E(X2) E(X)]?b. V(X)?c. The general relationship among the quantities E(X), E[X(X 1)], and V(X)?
6. The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with pdf f(x) k[1 (x 3)2] 2 x 4 0 otherwisea. Sketch the graph of f(x).b. Find the value of k.c. What is the probability that the actual tracking
5. A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is f(x) kx2 0 x 2 0 otherwisea. Find the
4. Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. The article “Blade Fatigue Life Assessment with Application to VAWTS” (J.Solar Energy Engr., 1982: 107–111) proposes the Rayleigh distribution, with pdf f(x; ) x2 e x2/(2 2) x
3. The error involved in making a certain measurement is a continuous rv X with pdf f(x) .09375(4 x2) 2 x 2 0 otherwisea. Sketch the graph of f(x).b. Compute P(X 0).c. Compute P(1 X 1).d. Compute P(X .5 or X .5).
2. Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A 5 and B 5.a. Compute P(X 0).b. Compute P(2.5 X 2.5).c. Compute P(2 X 3).d. For k satisfying 5 k k 4 5, compute P(k X k 4).
1. Let X denote the amount of time for which a book on 2-hour reserve at a college library is checked out by a randomly selected student and suppose that X has density function f(x) .5x 0 x 2 0 otherwise Calculate the following probabilities:a. P(X 1)b. P(.5 X 1.5)c. P(1.5 X)
43. Write a general rule for E(X c) where c is a constant.What happens when you let c , the expected value of X?
44. A result called Chebyshev’s inequality states that for any probability distribution of an rv X and any number k that is at least 1, P(⏐X ⏐ k) 1/k2. In words, the probability that the value of X lies at least k standard deviations from its mean is at most 1/k2.
45. If a X b, show that a E(X) b.?
47. Use Appendix Table A.1 to obtain the following probabilities:a. B(4; 15, .3)b. b(4; 15, .3)c. b(6; 15, .7)d. P(2 X 4) when X Bin(15, .3)e. P(2 X) when X Bin(15, .3)f. P(X 1) when X Bin(15, .7)g. P(2 X 6) when X Bin(15, .3)
48. When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let X the number of defective boards in a random sample of size n 25, so X Bin(25, .05).
35. A small market orders copies of a certain magazine for its magazine rack each week. Let X demand for the magazine, with pmf Suppose the store owner actually pays $1.00 for each copy of the magazine and the price to customers is $2.00. If magazines left at the end of the week have no salvage
34. Suppose that the number of plants of a particular type found in a rectangular region (called a quadrat by ecologists) in a certain geographic area is an rv X with pmf p(x) { c/x3 x 1, 2, 3, . . .0 otherwise Is E(X) finite? Justify your answer (this is another distribution that statisticians
24. An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X the number of months between successive payments. The cdf of X is as follows:
28. Show that the cdf F(x) is a nondecreasing function; that is, x1 x2 implies that F(x1) F(x2). Under what condition will F(x1) F(x2)?
a. What is the expected number of calls among the 25 that involve a fax message?
33. Let X be a Bernoulli rv with pmf as in Example 3.18.a. Compute E(X2).b. Show that V(X) p(1 p).c. Compute E(X79).
30. An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is
32. An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage space, respectively. Let X the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmfa. Compute E(X), E(X2), and V(X).b. If the price
What is the mean? Calculate based only on the valid responses.
Calculate the IQR for both groups. What do the IQRs reveal about the degree diversity for males and females?
What is the limitation to applying IQR to ordinal data?
What is the range of convictions in 1990? In 2009? Which is greater?
What is the mean number of convictions in 1990 and 2009?
Calculate the standard deviation for 1990 and 2009.
Which year appears to have more variability in number of convictions as measured by the standard deviation? Are the results consistent with what you found using the range?
Compare the range for the Western states with that of the Midwest. Which region had a greater range?
Examine the IQR for each region. Which is greater?
Use the statistics to characterize the variability in population increase of the elderly in the two regions. Does one region have more variability than another? If yes, why do you think that is?
Note that SPSS supplies the IQR, the median, and the minimum and maximum values of each group. Looking at the values of the mean and median, do you think the distribution of prestige is skewed for respondents with a high school diploma? For respondents with a bachelor’s degree? Why or why not?
Explain why you think there is more variability of prestige for either group, or why the variability of prestige is similar for the two groups.
What is the IQV for this variable? Do you find it to be higher (closer to 1) or lower (closer to 0) than you might have expected for political views? Or to put it another way, did you expect that Americans would be diverse in their political views or more narrowly concentrated in certain categories?
Calculate the sum of the squared percentages, or ∑Pct2.
Given your findings, is the distribution symmetrical, positively skewed, or negatively skewed?
In Exercise 7, you examined U.S. household size in 2010. Using these data, construct a histogram to represent the distribution of household size.1./ From the appearance of the histogram, would you say the distribution is positively or negatively skewed? Why?2./ Now calculate the median for the
Do these numbers provide further evidence to support your decision about how the distribution is skewed? Why do you think the distribution of household size is asymmetrical?
Do homicide rates vary with country population? Investigate this question using United Nation’s data for countries grouped by population size. Calculate the mean and median for each group. Describe the distribution for each group. Which group has the higher homicide rate?
The following table reports infant mortality rates for selected countries based on estimates reported in the Central Intelligence Agency’s 2016 World Factbook. Infant morality rates have been associated with the quality of prenatal care and the overall quality of health care provided within a
Explain the importance of measuring variability
Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation
Identify the relative strengths and weaknesses of the measures
How many categories (K) are we working with?
Calculate and interpret the range and the IQR. Which is a better measure of variability? Why?
Calculate and interpret the mean and standard deviation.
What number of television hours per day corresponds to a Z score of +1?
What is the percentage of people who watch between 1 and 6 hours of television per day?
If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights? If not, what number of shelter openings will be needed?
The current capacity is only 220 openings, because some shelters have been closed. What is the percentage of nights that the number of abused women seeking shelter will exceed current capacity?
If you have 13.77 years of education, that is, the mean number of years of education, what is your Z score?
If your friend is in the 60th percentile, how many years of education does she have?
How many people have between your years of education (13.77) and your friend’s years of education?
What is the percentile rank of a score of 172?
What is the Z score for a test score of 200?
What percentage of scores falls between 100 and 160?
What proportion of respondents should score above 190?
What proportion of people watch television less than 5 hours per day? How many does this correspond to in the sample?
What is the Z score for a person who watches more than 8 hours per day?
Identify two possible explanations for the variation in divorce rates across the 10 states
What are the means? The standard deviations?
Compare the mean with the standard deviation for each variable. Does there appear to be more variability in the number of crimes or in police expenditures per capita in these states? Which states contribute more to this greater variability?
Suggest why one variable has more variability than the other. In other words, what social forces would cause one variable to have a relatively large standard deviation?
The following table summarizes the racial differences in education and the ideal number of children for GSS 2010 Chinese Americans and Filipino Americans. Based on the means and standard deviations (in parentheses), what conclusions can be drawn about differences in the ideal number of children?
The 2015 average life expectancy for the total population is reported for 10 countries. Calculate the appropriate measures of central tendency and variability for both European countries and non-European countries. Is there more variability in life expectancy for European countries or non-European
Explain the importance and use of the normal distribution in statistics
Describe the properties of the normal distribution
Transform a raw score into standard (Z) score and vice versa
Transform a Z score into proportion (or percentage) and vice versa
Calculate and interpret the percentile rank of a score
Suppose an individual is in the 67th percentile in this test, what is his or her corresponding recidivism score?
Describe the five stages of the research process
Variables can be measured according to more than one level of measurement. For the following variables, identify at least two levels of measurement. Is one level of measurement better than another? Explain.1./ Individual age 2./ Annual income 3./ Religiosity 4./ Student performance 5./ Social class
Construct and analyze frequency, percentage, and cumulative distributions
Calculate proportions and percentages
Compare and contrast frequency and percentage distributions for nominal, ordinal, and interval-ratio variables
Create a bivariate table
Construct and interpret a pie chart, bar graph, histogram, the statistical map, line graph, and time-series chart
Identify the level of measurement for each variable.
Construct raw frequency tables for race.
What proportion of the 30 individuals is nonwhite? What percentage is white?
Which is the smallest perceived class group?
Which two classes include the largest percentages of people?
Construct measures of political participation at the nominal, ordinal, and interval-ratio levels. (Hint: You can use behaviors such as voting frequency or political party membership.) Discuss the advantages and disadvantages of each.
Define independent and dependent variables
Distinguish between the three levels of measurement
Apply descriptive and inferential statistical procedures
How will the Affordable Care Act influence the quality of health care?
Has support for same-sex marriage increased during the past decade?
Does race or ethnicity predict voting behavior?
What factors affect the economic mobility of female workers?
In your own words, explain the relationship of data (collecting and analyzing) to the research process. (Refer to Figure 1.1.)
Construct potential hypotheses or research questions to relate the variables in each of the following examples. Also, write a brief statement explaining why you believe there is a relationship between the variables as specified in your hypotheses.1./ Political party and support of the Affordable

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Essentials Of Social Statistics For A Diverse Society 3rd Edition Anna Y Leon Guerrero, Chava Frankfort Nachmias - Solutions

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