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bayesian statistics an introduction
Statistics A Tool For Social Research 9th Edition Joseph F Healey - Solutions
For each of the following confidence levels, determine the corresponding Z score.
f.s 6 N 220 X = 33b. Ps 0.37 N 522e. Ps 0.43 N 1049c. Ps 0.79 N 121f. Ps 0.63 N 300d. Ps 0.14 N 100
For each of the following sets of sample outcomes, construct the 99% confidence interval for estimating Pu.a. Ps 0.40b. N 548 s 9 N 620 X = 100 c.s 3 N 220 X = 20 d.s 50 N 329 X = 1020 e.s 1.2 N 105 X =
For each set of sample outcomes below, construct the 95% confidence interval for estimating m, the population mean.a.s 0.7 N 157 X = 5.2
Your sampling method is not truly random and/or the population is not arranged in random fashion.
This exercise is tedious but, if you want a more concrete and tangible understanding of sampling distributions and the two theorems presented in this chapter, then it may have a significant payoff. At the end of this problem are listed the ages of a population of college students (N 50). By a
Imagine that you had to gather a random sample(N 300) of the student body at your school. How would you acquire a list of the population? Would the list be complete and accurate? What procedure would you follow in selecting cases (that is, simple or systematic random sampling)? Would cluster
After taking the state merit examinations for the positions of school counselor and social worker, you receive the following information on the tests and on your performance. On which of the tests did you do better?
In a distribution of scores with a mean of 35 and a standard deviation of 4, which event is more likely:that a randomly selected score will be between 29 and 31 or that a randomly selected score will be between 40 and 42?
and the standard deviation is .33, which of the following GPAs would qualify?3.20, 3.21, 3.25, 3.30, 3.35
To be accepted into an honor society, students must have GPAs in the top 10% of the school. If the mean GPA is
The local police force gives all applicants an entrance exam and accepts only those applicants who score in the top 15% on this test. If the mean score this year is 87 and the standard deviation is 8, would an individual with a score of 110 be accepted?
The average number of drop-outs for a school district has been 305 per year with a standard deviation of 50. What is the probability that next year the number of drop-outs will bea. less than 250? ___________b. less than 300? ___________c. more than 350? ___________d. more than 400? ___________e.
For a math test on which the mean was 59 and the standard deviation was 4, what is the probability that a student randomly selected from this class will have a scorea. between 55 and 65? ___________b. between 60 and 65? ___________c. above 65? ___________d. between 60 and 50? ___________e. between
On the scale mentioned in problem 5.7, if a score of 40 or more is considered “highly prejudiced,” what is the probability that a person selected at random will have a score in that range?
A scale measuring prejudice has been administered to a large sample of respondents. The distribution of scores is approximately normal, with a mean of 31 and a standard deviation of 5. What percentage of the sample had scoresa. below 20? ___________b. below 40? ___________c. between 30 and 40?
If a distribution of test scores is normal, with a mean of 78 and a standard deviation of 11, what percentage of the area liesa. below 60? ___________b. below 70? ___________c. below 80? ___________d. below 90? ___________e. between 60 and 65? ___________f. between 65 and 79? ___________ g. between
At St. Algebra College, the 200 freshmen enrolled in introductory biology took a final exam on which their mean score was 72 and their standard deviation was 6. The following table presents the grades of 10 students. Convert each into a Z score and determine the number of people who scored higher
For a normal distribution where the mean is 50 and the standard deviation is 10, what percentage of the area isa. between the scores of 40 and 47? ___________b. above a score of 47? ___________c. below a score of 53? ___________d. between the scores of 35 and 65? ___________e. above a score of 72?
The senior class has been given a comprehensive examination to assess educational experience.The mean on the test was 74 and the standard deviation was 10. What percentage of the students had scoresa. between 75 and 85? ___________b. between 80 and 85? ___________c. above 80? ___________d. above
Assume that the distribution of a college entrance exam is normal, with a mean of 500 and a standard deviation of 100. For each of the following scores, find the equivalent Z score, the percentage of the area above the score, and the percentage of the area below the score.
Scores on a quiz were normally distributed and had a mean of 10 and a standard deviation of 3. For each of the following scores, find the Z score and the percentage of area above and below the score.
and reproduced here. Compare the standard deviation computed for freshmen with the standard deviation computed for seniors. What happened? Why? Does this change relate at all to what happened to the mean over the four-year period? How? What happened to the shapes of the underlying distributions?
At St. Algebra College, the math department ran some special sections of the freshman math course using a variety of innovative teaching techniques.Students were randomly assigned to either the traditional sections or the experimental sections, and all students were given the same final exam. The
You’re the governor of the state and must decide which of four metropolitan police departments will win the annual award for efficiency. The performance of each department is summarized in monthly arrest statistics as reported here. Which department will win the award? Why?
One of your goals as the new chief administrator of a large social service bureau is to equalize work loads within the various divisions of the agency. You have gathered data on caseloads per worker within each division. Which division comes closest to the ideal of an equalized workload? Which is
Listed here are the rates of abortion per 100,000 women for 20 states in 1973 and 1975.Describe what happened to these distributions over the two-year period. Did the average rate increase or decrease? What happened to the dispersion of this distribution? What happened between 1973 and 1975 that
Compute the range and standard deviation for the data presented in problem 3.14. The data are reproduced here. What would happen to the value of the standard deviation if you removed Los Angeles from this distribution and recalculated? Why?
Per capita expenditures for public transportation for 20 cities are reported here for 2000 and 2010.Compute a mean and standard deviation for each year, and describe the differences in expenditures for the five-year period
In problem 3.11, you computed measures of central tendency for the number of cars per 1000 population for eight nations. The scores are reproduced here.Compute the standard deviation for this variable, and write a paragraph summarizing the mean, median, and standard deviation.Number of Cars per
Data on several variables measuring overall heath and well-being for five nations are reported here for 2005, with projections to 2010. Are nations becoming more or less diverse on these variables? Calculate the mean, range, and standard deviation for each year for each variable. Summarize the
Labor force participation rates (percent employed), percent high school graduates, and mean income for males and females in 10 states are reported here. Calculate a mean and a standard deviation for both groups for each variable and describe the differences. Are males and females unequal on any of
a. Compute the standard deviation for the pretest and posttest scores that were used in problems 2.6 and 3.12. The scores are reproduced here. Taking into account all of the information you have on these variables, write a paragraph describing how the sample changed from test to test. What does SOC
In problem 3.8, you computed mean and median income for 13 Canadian provinces and territories in two separate years. Now compute the standard deviation and range for each year, and, taking account of the two measures of central tendency and the two measures of dispersion, write a paragraph
Compute the range and standard deviation of the following 10 test scores.66, 75, 69, 72, 84, 90, 96, 70, 55, 45
Compute the range and standard deviation of the following 10 scores. (HINT: It will be helpful to organize your computations as in Tables 4.4.)10, 12, 15, 20, 25, 30, 32, 35, 40, 50
The following table shows the major areas of study selected by the first-year college students living in two small dormitories. Compute the index of qualitative variation for the table. Which dorm is more diverse in terms of this variable?
The marital status of residents of four apartment complexes is reported here. Compute the index of qualitative variation (IQV) for each neighborhood.Which is the most heterogeneous of the four? Which is the least? (HINT: It may be helpful to organize your computations as in Table 4.2.)SOC
Professional athletes are threatening to strike because they claim that they are underpaid. The team owners have released a statement that says, in part, “The average salary for players was $1.2 million last year.”The players counter by issuing their own statement that says, in part, “The
You have compiled the following information on each of the graduates voted “most likely to succeed” by a local high school for a 10-year period.For each variable, find the appropriate measure of central tendency
A sample of 25 freshmen at a major university completed a survey that measured their degree of racial prejudice (the higher the score, the greater the prejudice).a. Compute the median and mean scores for these data.10 43 30 30 45 40 12 40 42 35 45 25 10 33 50 42 32 38 11 47 22 26 37 38 10b. These
For the test scores first presented in problem 2.6 and reproduced here, compute a median and mean for both the pretest and posttest. Interpret these statistics.
The following table lists the approximate number of cars per 1000 population for eight nations. Compute the mean and median for these data. Which is greater in value? Is there a positive skew in the data? How do you know?
As the head of a social services agency, you believe that your staff of 20 social workers is very much overworked compared to 10 years ago. The case loads for each worker are reported below for each of the two years in question. Has the average caseload increased? What measure of central tendency
The administration is considering a total ban on student automobiles. You have conducted a poll on this issue of 20 fellow students and 20 of the neighbors who live around the campus and have calculated scores for your respondents. On the scale you used, a high score indicates strong opposition to
Following are four variables for 30 cases from the General Social Survey. Age is reported in years. The variable happiness consists of answers to the question“Taken all together, would you say that you are (1)very happy (2) pretty happy, or (3) not too happy?”Respondents were asked how many sex
Find the appropriate measure of central tendency for each variable displayed in problem 2.5. Report each statistic as you would in a formal research report.SOC 82 PART I DESCRIPTIVE STATISTICS Marital Racial/ Attitude on Abortion Scale R
The following table lists the median family incomes for 13 Canadian provinces and territories in 2000 and 2006. Compute the mean and median for each year and compare the two measures of central tendency. Which measure of central tendency is greater for each year? Are the distributions skewed?In
For 15 respondents, data have been gathered on four variables (see the following table).a. Find and report the appropriate measure of central tendency for each variable.b. (This problem is optional.) For the variable age, construct a frequency distribution with interval size 5 and the first
The following table presents the annual personhours of time lost due to traffic congestion for a group of cities for 2007. This statistic is a measure of traffic congestion PA Annual Person-Hours of Time Lost to Traffic Congestion per City Year per Person Baltimore 25 Boston 22 Buffalo 5 Chicago 22
You have been observing the local Democratic Party in a large city and have compiled some information about a small sample of party regulars. Find PS CHAPTER 3 MEASURES OF CENTRAL TENDENCY 81 the appropriate measure of central tendency for each variable.Social No. of Years Marital Number of
A variety of information has been collected for all district high schools. Find the most appropriate measure of central tendency for each variable and summarize this information in a paragraph. (HINT: The level of 80 PART I DESCRIPTIVE STATISTICS FRESHMEN Out-ofRegion Pocket Cafeteria Student of
A variety of information has been gathered from a sample of college freshmen and seniors, including their region of birth; the extent to which they support legalization of marijuana (measured on a scale on which 7 strong support, 4 neutral, and 1 strong opposition); the amount of money they spend
A hospital administrator has been keeping track of the number of times patients developed staph infections following surgery. Early in the year, the administrator required all medical staff to read a booklet titled Fighting Staph, and tripled the number of handsanitizer wall dispensers throughout
Sixteen high school students completed a class to prepare them for the College Boards. Their scores were as follows.420 345 560 650 459 499 500 657 467 480 505 555 480 520 530 589 These same 16 students were given a test of math and verbal ability to measure their readiness for college-level work.
As part of an evaluation of the efficiency of your local police force, you have gathered the PA/CJ SOC GER Case Pretest Posttest A 8 12 B 7 13 C 10 12 D 15 19 E 10 8 F 10 17 G 3 12 H 10 11 Case Pretest Posttest I5 7 J 15 12 K 13 20 L4 5 M 10 15 N 8 11 O 12 20 Construct frequency distributions for
Twenty-five students completed a questionnaire that measured their attitudes toward interpersonal violence. Respondents who scored high believed that in many situations a person could legitimately use physical force against another person. Respondents who scored low believed that in no situation
Twenty-five residents of a community for senior citizens were asked to keep track of the number of hours they watched TV during the past week.20 2 12 7 32 7 10 7 13 17 14 15 15 9 27 5 21 4 7 6 2 18 10 5 11a. Construct a frequency distribution to display these data.b. What are the midpoints of the
A local youth service agency has begun a sex education program for teenage girls who have been referred by the juvenile courts. The girls were given a 20-item test for general knowledge about sex, contraception, and anatomy and physiology upon admission to the program and again after completing the
The scores of 15 respondents on four variables are as reported next. These scores were taken from a public opinion survey called the General Social Survey, or the GSS. This data set is used for the computer exercises in this text. Small subsamples from the GSS will be used throughout the text to
The numbers of homicides in five U.S. states and five Canadian provinces for the years 1997 and 2008 were as follows on top of the next page.a. Calculate the homicide rate per 100,000 population for each state and each province for each year.Relatively speaking, which state and which province had
The town of Shinbone, Kansas, has a population of 211,732 and experienced 47 bank robberies, 13 murders, and 23 auto thefts during the past year.Compute a rate for each type of crime per 100,000 population. (HINT: Make sure that you set up the fraction with size of population in the denominator.)
At St. Winnefred Hospital, the numbers of males and females in various job categories are as follows:Job Males Females Totals Doctor 83 15 98 Nurse 62 116 178 Orderly 151 12 163 Lab Technician 32 30 62 Administrator 12 1 13 Clerk 72 141 213 Totals 412 315 727 SOC Read each question carefully before
The tables that follow report the marital status of 20 respondents in two different apartment complexes. (HINT: Make sure that you have the correct numbers in the numerator and denominator before answering these questions. For example, problem 2.1a asks for “the percentage of respondents in each
For each of the first 20 items in the General Social Survey (see Appendix G), indicate the level of measurement and whether the variable is continuous or discrete.
For each of the following research situations, identify the level of measurement of all variables and indicate whether they are discrete or continuous. Also, decide which statistical applications are used: descriptive statistics (single variable), descriptive statistics (two or more variables), or
The following are descriptions of research projects.For each project, identify the independent and dependent variables, classify them in terms of level of measurement, and determine whether they are discrete or continuous.a. For a research project in a political science course, a student has
Following are brief descriptions of how researchers measured a variable. For each situation, determine the level of measurement of the variable and whether it is continuous or discrete.a. Race or ethnicity. Respondents were asked to check all that apply:________ Black ________ White ________
For each of the following items from a public-opinion survey, indicate the level of measurement and whether the variable will be discrete or continuous. (HINT:Remember that only interval-ratio-level variables can be continuous.)a. In what country were you born? ___________b. What is your age?
Distinguish between descriptive and inferential statistics. Describe a research situation that would use each type.
Find a research article in any social science journal.Choose an article on a subject of interest to you, and don’t worry about being able to understand all of the statistics that are reported.a. How much of the article is devoted to statistics?b Is the research based on a sample from some
In your own words, describe the role of statistics in the research process. Using the “wheel of science” as a framework, explain how statistics link theory with research.
Evaluate each of the following:a. (3 7)/10b. 3 7/10
Round off each of the following to two places beyond the decimal point:a. 17.17532b. 43.119c. 1076.77337d. 32.4641152301e. 32.4751152301
Complete each of the following:a. 17 (3) (4) (2)b. 15 3 (5) 2c. (27)(54)d. (113)(2)e. (14)(100)f. 34/2 g. 322/11 h.i. (17)2
For the set of scores (Xi) of 50, 55, 60, 65, and 70, evaluate each of the following expressions:Xi Xi 2( Xi)2
Complete each of the following:a. 17 3b. 17(3)c. (17)(3)d. 17/3e. (42)2f. 1113
Explain the limitations of partial and multiple regression analysis.
Calculate and interpret the multiple correlation coefficient (R2).
Find and interpret the least-squares multiple regression equation with partial slopes.
Compute and interpret partial correlation coefficients.
Cite and explain the limitations of elaborating bivariate tables.
Compute and interpret partial gamma.
Recognize and interpret direct, spurious or intervening, and interactive relationships.
Compute and interpret partial measures of association.
Construct and interpret partial tables.
Explain the purpose of multivariate analysis in terms of observing the effect of a control variable.
Test Pearson’s r for significance
Use regression and correlation techniques to analyze and describe a bivariate relationship in terms of the three questions introduced in Chapter 12.
Explain the concepts of total, explained, and unexplained variance.
Find and explain the least-squares regression line and use it to predict values of Y.
Calculate and interpret slope (b), Y intercept (a), and Pearson’s r and r 2.
Interpret a scatter gram.
Test gamma and Spearman’s rho for significance.
Use gamma and Spearman’s rho to analyze and describe a bivariate relationship in terms of the three questions introduced in Chapter 12.
Explain the logic of proportional reduction in error in terms of gamma.
Calculate and interpret gamma and Spearman’s rho.
Compute and interpret measures of association for variables measured at the nominal level.
Investigate a bivariate association by properly calculating percentages for a bivariate table and interpreting the results.
List and explain the three characteristics of a bivariate relationship: existence, strength, and pattern or direction.
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