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statistics informed decisions using data
Statistics A Tool For Social Research 3rd Canadian Edition Joseph Healey, Steven Prus - Solutions
4. Perform the chi square test using the five-step model and correctly interpret the results.
3. Explain the logic of hypothesis testing as applied to a bivariate table.
2. Explain the structure of a bivariate table and the concept of independence as applied to expected and observed frequencies in a bivariate table.
1. Identify and cite examples of situations in which the chi square test is appropriate.
9.9 SOC Does support for suicide (“death with dignity”)vary by social class? Is this relationship different in different nations? Small samples in three nations were asked if it is ever justified for a person with an incurable disease to take his or her own life. Respondents answered in terms
9.8 SOC A social survey was administered to a random sample of adults. A subsample of these adults, selected randomly, is shown below. Each respondent has been classified as either a city dweller, a suburbanite, or a rural dweller. Are there statistically significant differences by place of
9.7 GER Do older citizens lose interest in politics and current affairs? A brief quiz on recent headline stories was administered to random samples of respondents from each of four different age groups. Is there a significant difference? The data below represent numbers of correct responses.High
9.6 PS Does the rate of voter turnout vary significantly by the type of election? A random sample of electoral districts displays the following pattern of voter turnout by election type. Assess the results for significance.Municipal Provincial Federal 33 35 42 78 56 40 32 35 52 28 40 66 10 45 78 12
9.5 SOC Are sexually active teenagers any better informed about AIDS and other potential health problems related to sex than teenagers who are sexually inactive? A 15-item test of general knowledge about sex and health was administered to random samples of teens who are sexually inactive, teens who
9.4 CJ Two separate crime reduction programs have been implemented in the city of Pearson, Ontario.One involves a neighbourhood watch program with citizens actively involved in crime prevention. The second involves officers patrolling the neighbourhoods on foot rather than in patrol cars. In terms
9.3 SOC In a local community, a random sample of 18 couples has been assessed on a scale that measures the extent to which power and decision making are shared (lower scores) or monopolized by one party (higher scores) and on marital happiness(lower scores indicate lower levels of unhappiness).The
9.2 SOC What type of person is most involved in the neighbourhood and community? Who is more likely to volunteer for organizations such as Scouts, Big Sisters, or the United Way? A random sample of 15 people have been asked for their number of memberships in community voluntary organizations and
9.1 Calculate the obtained F ratio for each set of scores below. (HINT: Follow the computational shortcut outlined in Section 9.4 and keep track ofa. Category A B C 5 10 12 7 12 16 8 14 18 9 15 20 all sums and means by constructing computational tables like Table 9.3 or 9.4.)
5. Explain the difference between the statistical significance and the importance of relationships between variables.
4. Define and explain the concepts of population variance, total sum of squares, sum of squares between, sum of squares within, and mean square estimates.
3. Perform the ANOVA test, using the five-step model as a guide, and correctly interpret the results.
2. Explain the logic of hypothesis testing as applied to ANOVA.
1. Identify and cite examples of situations in which ANOVA is appropriate.
8.15 SOC Some results from a recent social survey administered to a random sample of adults are reported below in terms of differences by sex.Which of these differences, if any, are significant?Write a sentence or two of interpretation for each test.a. Proportion favouring the legalization of
8.14 CJ The local police chief started a “crimeline”program some years ago and wonders if it’s really working. The program publicizes unsolved violent crimes in the local media and offers cash rewards for information leading to arrests. Are “featured” crimes more likely to be cleared by
8.13 SOC At Algebra University, the sociology and psychology departments have been feuding for years about the respective quality of their programs.In an attempt to resolve the dispute, you have gathered data about the graduate school experience of random samples of both groups of majors. The
8.12 SW A large counselling centre needs to evaluate several experimental programs. Write a paragraph summarizing the results of these tests. Did the new programs work?a. One program is designed for divorce counselling;the key feature of the program is its counsellors, who are married couples
8.11 CJ About half of the police officers in Pearson, Ontario, have completed a special course in investigative procedures. Has the course increased their efficiency in clearing crimes by arrest? The proportions of cases cleared by arrest for samples of trained and untrained officers are reported
8.10 For each problem, test the sample statistics for the significance of the difference. (HINT: In testing proportions, remember to begin with Formula 8.7, then solve Formulas 8.8 and 8.10.)a.Sample 1 Sample 2 Ps1 5 0.17 Ps2 5 0.20 n1 5 101 n2 5 114 b.Sample 1 Sample 2 Ps1 5 0.62 Ps2 5 0.60 n1 5
8.9 SOC A survey has been administered to random samples of respondents in each of five nations.For each nation, are men and women significantly different in terms of their reported levels of satisfaction?Respondents were asked: “How satisfied are you with your life as a whole?” Responses
8.8 SW As the director of the local youth club, you have claimed for years that membership in your club reduces juvenile delinquency. Now, a cynical member of your funding agency has demanded proof of your claim. Fortunately, your local sociology department is on your side and springs to your aid
8.7 SOC Are senior citizens who live in retirement communities more socially active than those who live in age-integrated communities? Write a sentence or two explaining the results of these tests.(HINT: Remember to use the proper formulas for small sample sizes.)a. A random sample of senior
8.6 SOC Are university students who live in residence significantly more involved in campus life than students who commute to campus? The data below report the average number of hours per week that students devote to extracurricular activities.Is the difference between these randomly selected
8.5 SOC Are middle-class families more likely than working-class families to maintain contact with relatives? Write a paragraph summarizing the results of these tests.a. A sample of middle-class families reported an average of 7.3 visits per year with close relatives, while a sample of
8.4 PA A number of years ago, the fire department in Pearson, Ontario, began recruiting females through an employment equity program. In terms of efficiency ratings as compiled by their superiors, how do the employment equity employees rate?The ratings of random samples of both groups were
8.3 SOC Do athletes in different sports vary in terms of intelligence? Below are aptitude test scores of random samples of university varsity hockey and soccer players. Is there a significant difference?Write a sentence or two explaining the difference.a. Sample 1 (Hockey Players)Sample 2 (Soccer
8.2 SOC Questionnaires were administered to samples of undergraduate students. Among other things, those questionnaires contained a scale that measured attitudes towards interpersonal violence(higher scores indicated greater approval of interpersonal violence). Test the results as reported below
8.1 For each problem below, test for the significance of the difference in sample statistics using the fivestep model. (HINT: Remember to solve Formula 8.4 before attempting to solve Formula 8.2. Also, in Formula 8.4, perform the mathematical operations in the proper sequence. First square each
6. List and explain each of the factors (especially sample size) that affect the probability of rejecting the null hypothesis and explain the differences between statistical significance and importance.
5. Conduct a two-sample hypothesis test using confidence intervals.
4. Perform a test of hypothesis for two-sample means or two-sample proportions following the five-step model and correctly interpret the results.
3. Explain what an independent random sample is.
2. Explain the logic of hypothesis testing as applied to the two-sample case.
1. Identify and cite examples of situations in which the two-sample test of hypothesis is appropriate.
7.18 The following essay questions review the basic principles and concepts of inferential statistics.The order of the questions roughly follows the five-step model.a. Hypothesis testing or significance testing can be conducted only with a random sample.Why?b. Under what specific conditions can it
7.17 PA The city manager of Pearson, Ontario, has received a complaint from the local union of firefighters that they are underpaid. Not having much time, the city manager gathers the records of a random sample of 27 firefighters and finds that their average salary is $38,073 with a standard
7.16 SW You are the head of an agency seeking funding for a program to reduce unemployment among teenage males. Nationally, the unemployment rate for this group is 18%. A random sample of 323 teenage males in your area reveals an unemployment rate of 21.7%. Is the difference significant? Can you
7.15 SOC/SW A researcher has compiled a file of information on a random sample of 317 families in a city that has chronic, long-term patterns of child abuse. Below are reported some of the characteristics of the sample along with values for the city as a whole. For each trait, test the null
7.14 CJ Provincially, the police clear by arrest 35%of the robberies and 42% of the aggravated assaults reported to them. A researcher takes a random sample of all the robberies (n 5 207)and aggravated assaults (n 5 178) reported to a metropolitan police department in one year and finds that 83 of
7.13 PS In a recent provincial election, 55% of the voters rejected a proposal to institute a new provincial lottery. In a random sample of 150 voters from rural communities, 49% rejected the proposal. Is the difference significant? Summarize your conclusions in a sentence or two.
7.12 CJ A random sample of 113 convicted sex offenders in a provincial prison system completed a program designed to change their attitudes toward women, sex, and violence before being released on parole. Fifty-eight eventually became repeat sex offenders. Is this recidivism rate significantly
7.11 GER/CJ A survey shows that 10% of the population is victimized by property crime each year.A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 14%. Are older people more likely to be victimized?Conduct a one-tailed test of significance.
7.10 PA Nationally, the per capita property tax is$130 per month. A random sample of 36 western cities averages $98 per month with a standard deviation of $5. Is the difference significant?Summarize your conclusions in a sentence or two.
7.9 SOC A random sample of 26 sociology graduates in BC scored an average of 458 on the GRE Advanced Sociology test with a standard deviation of 20. Is this significantly different from the national average (m 5 440)?
7.8 SOC A school system has assigned several hundred“chronic and severe underachievers”to an alternative educational experience. To assess the program, a random sample of 35 has been selected for comparison with all students in the system.a. In terms of GPA, did the program work?Systemwide GPA
7.7 SOCa. Nationally, the population as a whole watches an average of 6.2 hours of TV per day. A random sample of 1,017 senior citizens reports watching an average of 5.9 hours per day with a standard deviation of 0.7. Is the difference significant?b. The same sample of senior citizens reports that
7.5 SOC A random sample of 423 Albertans has finished an average of 12.7 years of formal education with a standard deviation of 1.7. Is this significantly different from the national average of 12.2 years?7.6 SOC A sample of 105 workers in the Roadster Division of the Toy Car Factory earns an
7.4 SOC Nationally, the average score on the GRE(Graduate Record Examinations) verbal test is 453 with a standard deviation of 95. A random sample of 152 first-year graduate students entering Algebra University shows a mean score of 502. Is there a significant difference?
7.3 SWa. Nationally, social workers average 10.2 years of experience. In a random sample, 203 social workers in the greater metropolitan area of Pearson, Ontario, average only 8.7 years with a standard deviation of 0.52. Are social workers in Pearson, Ontario, significantly less experienced? (HINT:
7.2 SOCa. The student body at Algebra University attends an average of 3.3 parties per month. A random sample of 117 sociology majors averages 3.8 parties per month with a standard deviation of 0.53. Are sociology majors significantly different from the student body as a whole?(HINT: The wording of
7.1a. For each situation, find Z (critical).Alpha Form Z (Critical)0.05 One-tailed 0.10 Two-tailed 0.06 Two-tailed 0.01 One-tailed 0.02 Two-tailedb. For each situation, find the critical t score.Alpha Form n t (Critical)0.10 Two-tailed 31 0.02 Two-tailed 24 0.01 Two-tailed 121 0.01 One-tailed 31
8. Conduct a single-sample hypothesis test using a confidence interval.
7. Define and explain Type I and Type II errors and relate each to the selection of an alpha level.
6. Explain the difference between one- and two-tailed tests and specify when each is appropriate.
5. Test the significance of single-sample means and proportions using the five-step model and correctly interpret the results.
4. Identify and cite examples of situations in which one-sample tests of hypotheses are appropriate.
3. Explain what it means to “reject the null hypothesis” or “fail to reject the null hypothesis.”
2. Define and explain the conceptual elements involved in hypothesis testing, especially the null hypothesis, the sampling distribution, the alpha level, and the test statistic.
1. Explain the logic of hypothesis testing.
6.19 SOC The results listed below are from a survey given to a random sample of the Canadian public. For each sample statistic, construct a confidence interval estimate of the population parameter at the 95% confidence level. Sample size (n) is 2,987 throughout.a. The average occupational prestige
6.18 SOC You are the consumer affairs reporter for a daily newspaper. Part of your job is to investigate the claims of manufacturers, and you are particularly suspicious of a new economy car that the manufacturer claims will get 3.0 L/100 km. After checking the mileage figures for a random sample
6.17 SOC The fraternities and sororities at Algebra University have been plagued by declining membership over the past several years and want to know if the incoming first-year students will be a fertile recruiting ground. Not having enough money to survey all 1,600 first-year students, they
6.16 SOC The World Values Survey is administered periodically to random samples from societies around the globe. Below are listed the number of respondents in each nation who said that they are “very happy.” Compute sample proportions and construct confidence interval estimates for each nation
6.15 PS Two individuals are running for mayor of Pearson, Ontario. You conduct an election survey a week before the election and find that 51%of the respondents prefer candidate A. Can you predict a winner? Use the 99% level. (HINT: In a two-candidate race, what percentage of the vote would the
6.14 For each of the three sample sizes below, construct the 95% confidence interval. Use a sample proportion of 0.40 throughout. What happens to interval width as sample size increases? Why?Ps50.40 Sample A: n5100 Sample B: n51,000 Sample C: n510,000
6.13 For the sample data below, construct four different interval estimates of the population mean, one each for the 90%, 95%, 99%, and 99.9% level.What happens to the interval width as confidence level increases? Why?X5100 s510 n5500
6.12 SW A random sample of 100 patients treated in a program for alcoholism and drug dependency over the past 10 years was selected. It was determined that 53 of the patients had been readmitted to the program at least once. At the 95% level, construct an estimate for the population proportion.
6.11 SOC A random sample of 1,496 respondents of a major metropolitan area was questioned about a number of issues. Construct estimates for the population at the 90% level for each of the results reported below. Express the final confidence interval in percentages (e.g., “between 40 and 45%
6.10 PA random sample of 324 residents of a community revealed that 30% were very satisfied with the quality of trash collection. At the 99% level, what is your estimate of the population value?
6.9 SOC The survey mentioned in Problem 6.5 found that 25 of the 178 households consisted of unmarried couples who were living together.What is your estimate of the population proportion?Use the 95% level.
6.8 CJ A random sample of 500 residents of Pearson, Ontario, shows that exactly 50 of the respondents had been the victims of violent crime over the past year. Estimate the proportion of victims for the population as a whole, using the 90% confidence level. (HINT: Calculate the sample proportion Ps
6.7 SOC A random sample of 429 university students was interviewed about a number of matters.a. They reported that they had spent an average of $178.23 on textbooks during the previous semester. If the sample standard deviation for these data is $15.78, construct an estimate of the population mean
6.6 SOC A random sample of 100 television programs contained an average of 2.37 acts of physical violence per program. At the 99% level, what is your estimate of the population value? Construct an error bar to display your results.X 5 2.37 s 5 0.30 n 5 100
6.5 SOC A researcher has gathered information from a random sample of 178 households. For each variable below, construct confidence intervals to estimate the population mean. Use the 90% level.a. An average of 2.3 people resides in each household. Standard deviation is 0.35.b. There was an average
6.4 SW You have developed a series of questions to measure “burnout” in social workers. A random sample of 100 social workers working in the greater metropolitan area of Pearson, Ontario, has an average score of 10.3, with a standard deviation of 2.7.At the 95% level, what is your estimate of
6.3 For each confidence level below, determine the corresponding Z score.Confidence Level (%) Alpha Area Beyond Z Z Score 95 0.05 0.0250 1.96 94 92 97 98 99.9
6.2 For each set of sample outcomes below, construct the 99% confidence interval for estimating Pu.a. Ps 5 0.14b. Ps 5 0.37c. Ps 5 0.79 n 5 100 n 5 522 n 5 121d. Ps 5 0.43e. Ps 5 0.40f. Ps 5 0.63 n 5 1049 n 5 548 n 5 300
6.1 For each set of sample outcomes below, construct the 95% confidence interval for estimating μ, the population mean.a. X 55.2b. X 5100c. X 520 s 5 0.7 s 5 9 s 5 3 n 5 157 n 5 620 n 5 220d. X 51,020e. X 57.3f. X 533 s 5 50 s 5 1.2 s 5 6 n 5 329 n 5 105 n 5 220
6. Determine the number of people needed in a sample to get a desired confidence interval.
5. Explain the relationships between confidence level, sample size, and the width of the confidence interval.
4. Use the error bar to graph a confidence interval.
3. Construct and interpret confidence intervals for sample means and sample proportions.
2. Define and explain the concepts of bias and efficiency.
1. Explain the logic of estimation and the role of the sample, sampling distribution, and population.
3. Your sampling method is not truly random and/or the population is not arranged in random fashion.17 20 20 19 20 18 21 19 20 19 19 22 19 23 19 20 23 18 20 20 22 19 19 20 20 23 17 18 21 20 20 18 20 19 20 22 17 21 21 21 21 20 20 20 22 18 21 20 22 21
2. Sample size (2) is too small. An n of 5 or 10 would work much better.
1. You didn’t take enough samples. You may need as many as 100 or 200 (or more) samples to see the curve begin to look “normal.”
5.1 This exercise is extremely tedious and hardly ever works out the way it ought to (mostly because not many people have the patience to draw an“infinite” number of even very small samples).However, if you want a more concrete and tangible understanding of sampling distributions and the two
4. Explain the two theorems presented.
3. Differentiate between the sampling distribution, the sample, and the population.
2. Explain the principle of random sampling and these key terms: population, sample, parameter, statistic, representative, and EPSEM.
1. Explain the purpose of inferential statistics in terms of generalizing from a sample to a population.
4.14 To be accepted into a university’s co-op education program, students must have GPAs in the top 10% of the school. If the mean GPA is 2.78 and the standard deviation is 0.33, which of the following GPAs would qualify?3.20, 3.21, 3.25, 3.30, 3.35
4.12 After taking a city’s merit examinations for the positions of social worker and employment counsellor you receive the following information on the tests and on your performance. On which of the tests did you do better?Social Worker Employment Counsellor X 5118 X 527 s 5 17 s 5 3 Your score 5
4.11 The local police force gives all applicants an entrance exam and accepts only those applicants who score in the top 15% on the exam. If the mean score this year is 87 and the standard deviation is 8, would an individual with a score of 110 be accepted?
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