The NCVS samples approximately 200,000 of American households. A random sample of 50 cases were drawn from the NCVS and

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The NCVS samples approximately 200,000 of American households. A random sample of 50 cases were drawn from the NCVS and the data is provided below. Although the NCVS includes many variables that measure victimization and crime, only education, race, household income and the number of victimization reports are provided in the table below. 201 Education is coded based on the highest level of education completed. Race is coded white and non- white, such that those Asians, for instance, would be classified as non-white Household income is coded as <$19,000, $19,000-$39,999, or $40,000+ Reports captures the number of victimization reports. CASE EDUCATION REPORTS RACE whote HOUSEHOLD INCOME $40,000+ I 6 2 14 white $40,000+ 4 3 16 white 540,000+ 1 4 9 white $19,000 4 10 white $19,000-$39.999 1 12 white $19,000 2 16 white $40,000+ 2 18 non-white $40,000 3 11 white $40,000+ 2 12 white $40,000 4 14 whote $40,000+ 4 16 white $19.000-539.999 4 16 white $19.000-539.999 4 12 white $19,000 12 white $19.000 12 white 16 white 12 white 10 white 14 non-white 12 white 18 while 14 non-white 12 non-white white 18 12 white 12 white 14 white non-white white white white white white white white white while white white white what white non-white white white non-white white while 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 14 14 12 14 18 12 14 16 9 16 16 16 14 12 16 10 18 14 18 14 16 12 $40,000 $40,000+ $19,000-$39.999 $40,000+ $40,000 <$19,000 $40,000+ $40,000+ $19,000 $40,000+ $19,000-$39,999 $19,000 $40,000 <$19.000 $40,000 $19,000 $40,000 $40,000+ $19,000-$39.999 $19,000 $40,000+ $40,000+ $40,000+ $40,000 <$19,000 $19,000-$39,999 $40,000 540,000+ <<$19,000 540,000+ <$19.000 $40,000 $40,000+ $19,000-$39.999 $40,000+ 2 1 3 1 2 1 2 4 3 1 3 S 4 2 2 3 ¡ 1 3 4 4 2 2 3 2 2 2 1 2 3 3 3 2 1 1 3 4
SOCIOL 352: Criminological Statistics and Data Analysis NAME: Problem Set, Part Two Did not show work Turned in late 5. Now that you have descriptive information about the sample, determine how well the sample represents the population from which it was selected. The population size was 500 that the sample of 50 was drawn from. a. What would have happened if you had selected a different sample of 50 people? What would have changed? b. Will you be able to use the sample statistics to estimate the true population parameter? Why or why not? c. Will you be able to use the sample statistics to state with 100% accuracy the actual population parameter? Why or why not? 6. Previously you computed the mean for the average number of years of education and the average number of victimization reports. Now use confidence intervals to estimate the actual education attainment and victimization reports for the population. a. Education Construct the 90% confidence interval: 1
Interpret the 90% confidence interval. b. Reports Construct the 80% confidence interval: Construct the 95% confidence interval: Compare the 80% confidence interval to the 95% confidence interval. 7. Test the following hypotheses a. You know that the average number of years of education for the national population is 12.5 years, with a standard deviation of 1.5 years. You hypothesize that the sample's average number of years of education is different from the national population's average. What type of hypothesis test would this require, one-tailed or two-tailed? In proper notation, what would the null hypothesis be? In proper notation, what would the research hypothesis be? To test this hypothesis would you use a Z or attest? What is the test statistic (include degrees of freedom if necessary)?
Assuming an alpha of .05, what is the p-or critical value needed to reject the null hypothesis? What is your conclusion? b. You know the average number of victimization reports for the population is 1, but don't know the standard deviation. You hypothesize that your sample has more victimization reports than the national population. What type of hypothesis test would this require, one-tailed or two-tailed? In proper notation, what would the null hypothesis be?__ In proper notation, what would the research hypothesis be? To test this hypothesis would you use a Z or attest? What is the test statistic (include degrees of freedom if necessary)? Assuming an alpha of .05, what is the p-or critical value needed to reject the null hypothesis? What is your conclusion and interpretation?
8. To determine if there is a relationship between the variables, construct bivariate tables by filling in the percentages cells of each table (round to the second decimal place). Table 1. Years of Education by Race Race Years of Education White Non-white 10 years or less 11-12 years 13-14 years 15-16 years 17-18 years Total N Total% Table 2. Number of Victimization Reports by Household Income Reports <$19,000 1 2 3 4+ Total N Total% Table 3. Number of Victimization Reports by Years of Education Reports 10 or less 11-12 1 Total N Total% b. Is there evidence of a relationship in Table 1 (Yes/No)? c. Is there evidence of a relationship in Table 2 (Yes/No)? d. Is there evidence of a relationship in Table 3 (Yes/No)? 2 3 4+ Household Income $19,000-$39,999 Years of Education 13-14 15-16 $40,000+ 17-18
e. In the table below, calculate chi-square based on Table 3 (Number of Victimization Reports by Years of Education). (S-1)² fo fe fo-fe (fo-fe)² X²= f. Based on an alpha of.01, do you reject the null hypothesis? 9. What is one conclusion you can draw about the hypothesized relationships among the variables? 10. What is one suggestion you could make to improve this study?