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RECOMMENDED WEB EXERCISES Chapter 1 Chapter 1 of the textbook offers a broad overview of the research process, and lays the groundwork for your future understanding of statistical data analysis. Contrary to what you may think, people actually do use statistics on a daily basis, for a wide variety of purposes. To learn more about some organizations that do utilize statistical analysis during their research efforts, visit some of the websites shown below. You should also find other websites by using your search engine to locate more organizations that do polling, surveys, market research, and other forms of data analysis. What are some of the uses to which you found statistics being employed? How many organizations did you find that are involved in data analysis? Were you surprised at the number? 1. U. S. Bureau of the Census Report to Congress - The Plan for Census 2000 (July 1997) http://www.census.gov/main/www/surveys.html 2. The Gallup Organization "How Polls are Conducted"http://www.gallup.com 3. The Roper Center for Public Opinion Research http://www.ropercenter.uconn.edu/4. U. S. Department of Labor Bureau of Labor Statistics 5. National Opinion Research Center "Capabilities" 6. General Social Survey http://www.icpsr.umich.edu/GSS/ After you have investigated these websites, pick a topic that interests you (examples might be the rate of teen pregnancy or educational attainment by race or household income) and search the web to find data related to that topic. What websites did you locate? What kinds of data did you find? Did the data provide factual information about the topic? Did you find data that expressed people's opinions on the topic? When would these different kinds of data be useful? Chapter 2 The U. S. Census Bureau collects a tremendous amount of data about people of Hispanic origin in the United States. Search the web (at http://www.census.gov, and then search the census website for "Hispanic") to find out how many distinct groups make up the Hispanic category in census data. Construct a frequency distribution for the total population of each group. Now construct a percentage distribution of the different population numbers. Show the proportions of each group to the total Hispanic population. What other information contained in the Census Bureau data is relevant to your analysis?
Find data on the web about the number of adherents to different religious beliefs in the world. Some websites that offer data on this topic include http://www.academicinfo.net/religindex.html, http://www.adherents.com/, http://www.aril.org/World.html, and http://www.geocities.com/Athens/Forum/1699/. Present these data in a variety of formats, as discussed in Chapter 3 of the text (for example, pie chart, bar graph, statistical map, and histogram). Which format seems to present the data in the most understandable manner? Why? If the data you gathered from the web had been the percentage of believers in different faiths in each country, would your choice of graphic formats remain the same? Why or why not? If the data you collected included more detail about the number of believers (such as sex, age, educational attainment, political affiliation, etc.), how would you choose to present that data graphically?
Search the web to find the numbers of female and male participants in all NCAA sports programs. This information can be found at http://www2.ncaa.org, then select "Site Index" and "Participation rates." Pick a particular division of NCAA schools (I, II, or III) and sex of participant. Find the median number of athletes participating in a specific sport. Calculate the mean number of participants per sport. Which sport is the mode? Which measure of central tendency best represents the data set you are using? Why that one? How is the distribution you picked shaped? What are some reasons that the distribution is skewed in the direction it is (if it is skewed)? Repeat the same analysis with the "other" sex. Compare the measures of central tendency for males and females. Does there appear to be large difference between the two measures? Chapter 5 Use the Internet to find the population of ten towns and/or cities in your home state and two neighboring states. The Census Bureau lists the most current populations for every city and town in the country at http://www.census.gov/popest/. Randomly select the ten towns or cities from each state. Using your lists, calculate the variance, standard deviation, and interquartile range for each of the three states. Compare the measures of variability you calculated. Does your home state contain more or less variability than the states you compared it to? Why might someone want to know how much variation exists in the population figures? What are some of the implications for state and local governments of these measures of variability? Which measure of variability would you recommend for this purpose? Why?
The U. S. Census Bureau gathers data each calendar quarter concerning home ownership in the United States and reports it at http://www.census.gov/hhes/www/housing/hvs/q202prss.pdf. In this report, find data that shows home ownership by race and ethnicity or home ownership by age of householder. Choose the data set that seems more interesting to you and construct a bivariate table for the most recent quarter reported, and analyze the data. How strong is the relationship between the two variables? What direction does the relationship between age and home ownership have? Can a direction be determined for the relationship between race/ethnicity and home ownership? Why or why not? Which variable did you consider to be the independent variable? Why? What other control variables might be included in the analysis to make it more informative? Can you think of any reason why the relationship you discovered (if any) might be spurious? How could you test for spuriousness of the relationship between age and home ownership or between race/ethnicity and home ownership?
PollingReport.com is an independent, nonpartisan resource on trends in American public opinions. One survey reported respondents' favorite women's sport to watch ( http://www.pollingreport.com/sports.htm#Women's). Select at least five sports and construct a table that summarizes the percentage of men and women that name that sport as their favorite. Do the data consist of nominal or ordinal variables? Assume that half of the sample was women and the other half was men (if there is an odd number in the sample, assume that there was one more woman than men). Calculate the appropriate measure of association between men's and women's opinions. Is the relationship a strong one? What direction does the relationship show? What control variables would you recommend introducing to the analysis? Chapter 8 Example #1: Find data on the web that shows the amount of education expenditures per student and the dropout rates for each state in the United States. Both of these are available on the U.S. Census Bureau website (http://www.census.gov). Construct a scatter diagram using this data. Does there appear to be a relationship between the two variables? If so, what type of relationship? What direction does the relationship appear to have? Calculate the value of the Pearson correlation coefficient, using expenditures per student as the predictor. Calculate the best-fitting straight-line equation, variance, covariance, and coefficient of determination for the data. Formulate the regression equation and solve for a and b . Interpret the regression equations. Based on your analysis, characterize the relationship between these two variables. Example #2: One measure of social welfare is life expectancy at birth. The Population Reference Bureau ( http://www.prb.org/ ) collects this data for virtually every country (however some countries do not provide complete data sets to PRB). Click on "Data Finder" to access information about life expectancy for the world as a whole. One variable affecting life expectancy appears to be sex. Now find life expectancy for men and for women. Note the difference in life expectancy for males and females. Other factors that may affect life expectancy include the number of baby-friendly health facilities, GNI PPP per capita (a measure of per capita income), median age (in months) at introduction of complementary foods, and the median duration of any breastfeeding. Select one of these other factors (that seems to you to be likely to affect life expectancy) and collect data for it and overall life expectancy in ten randomly selected countries. If the data are not available for one or more of the countries you picked, select substitute countries. Construct a scatter diagram using these data. Does there appear to be a relationship between the two variables? If so, what type of relationship? What direction does the relationship appear to have? Calculate the value of the Pearson correlation coefficient, using the factor you chose as the predictor for life expectancy. Use ANOVA to test the statistical significance of R square. Calculate the best-fitting straight-line equation, variance, covariance, and coefficient of determination for the data. Based on your analysis, characterize the relationship between the two variables you chose.
Chapter 9 in the text suggests that the scores on the Scholastic Aptitude Test (SAT) approach a normal distribution. The College Board developed, administers, and reports the results of the SAT at http://www.collegeboard.com. Its report for high school seniors who graduated in 2002 is shown at http://www.collegeboard.com/prod_downloads/about/news_info/cbsenior/yr2004/CBS2004Report.pdf Find the mean verbal and math scores for all people who took the test in 2002 and compare those to the mean scores by race and ethnicity shown in Table 7. Calculate the Z score for each racial or ethnic group shown in Table 7. Now do the same for several states of interest in Table 3. Transform the Z scores into proportions. If you took the SAT (and remember your score!), calculate the percentile at which you would be in the class of 2004. Is this different than your percentile in the year you took the test? If so, why would it be different?Chapter 10 The WNBA is a professional basketball league featuring the best female athletes in this sport. Visit the WNBA's website at http://www.wnba.com/index_new.html and select "Players." All of the players in the league are listed alphabetically on this web page. Randomly select twenty players (how can you be sure your selection is indeed random?). Calculate the mean height and mean weight for the sample you selected. Calculate the standard error of the mean for both height and weight in your sample. What does the central limit theorem suggest about your sample of twenty players? Does this sample accurately represent the population from which it is drawn? How is the population defined in this case? Is this sample representative of the overall population of females? Why or why not? Chapter 11 The U. S. Census Bureau collects a wide variety of information about American residents, one of which is annual income earned by individuals. Go to the Census Bureau website ( http://www.census.gov ) and under the "People" heading, click on "Income." Select "Detailed Income Tabulations" and "Person" for the most recent survey. Select one of the tables showing the relationship between education attainment and income. Using the standard error of the mean data shown at the bottom of the table, calculate the confidence intervals for five of the educational attainment categories. Was all of the information you needed to calculate the confidence interval available in the table? Now review some of the other tables from the "Person" listing. Do the confidence intervals you calculated for your original table also hold for the new table you are reviewing? Why or why not? What factors appear to influence earning capacity other than educational attainment?
Contraceptive use among married and single women varies widely among countries of the world. The Population Reference Bureau ( http://www.prb.org/ ) tracks this usage in its annual World Population Data Sheet. Click on "Data Finder" on this website and look at the factors under "Population and Health Variables" that the Population Reference Bureau associates with contraceptive use. Make a list of these factors and think about how they may affect the use of contraception. Formulate a research hypothesis and null hypothesis for each of these factors. Collect data with which to test your hypothesis (be aware that not all countries report all of the data requested by the Population Reference Bureau, so you may have to choose additional countries from which to collect data). Does the country in which the females reside affect contraceptive use? Determine the degrees of freedom associated with your model, and calculate the t statistic. Calculate the estimated standard error for your sample. Should you use one-tailed or two-tailed tests? What level of alpha should you use? Interpret the results of your tests. Were your hypotheses supported by the tests you performed? Describe the risks of making a Type I error when interpreting the results of your calculations? What did you learn about contraceptive use among women?
Go back to the bivariate table you constructed in the exercise for Chapter 6, comparing home ownership rates by age of householder or race/ethnicity. Conduct a Chi-Square test for statistical independence Do the relationships appear to be independent? Search this website to find details about sample size and sampling techniques. How does the sample size affect your conclusion? Does there appear to be substantive significance to your findings? Chapter 14 Think of a research question that interests you (this may be the same topic that you investigated in the Chapter 1 exercise) and that requires the use of ANOVA. Formulate the necessary hypotheses related to your research question. What are the independent and dependent variables in your hypotheses? What were your research and null hypotheses? What assumptions did you make about your samples? What alpha did you select? Which sampling distribution and test statistic did you use? Did the data you collected allow you to calculate the test statistic you selected? How could ANOVA applications be applied to your research question? Conduct the appropriate ANOVA analyses for your data. How does the use of ANOVA applications affect your decision about the results of your original tests? Did your interpretation change as a result of using ANOVA analysis?
Think of a research question that interests you (this may be the same topic that you investigated in the Chapter 1 exercise). A good way to approach this is to think of something about which you are curious and would like to know more. Formulate at least three hypotheses related to your research question. What are the independent and dependent variables in your hypotheses? Briefly summarize the theory(ies) that supports your hypotheses. Find data on the web that informs your hypotheses (if you are researching the same topic as you did in Chapter 1, revisit the websites you found there and others). Organize the data you collect into a frequency distribution and construct a graphic display that clearly exhibits the data. Calculate the measures of central tendency for your data. Which measure best represents the data? Calculate measures of variability for the data and analyze your findings. Finally, describe the relationships between variables you discover, using the appropriate measures of association. If sufficient data are not available to complete your research, identify the variables that you would need to measure, their level of measurement, and how the variables could be measured. Reviewing Inferential Statistics
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