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Labor union membership Essay Research Question: Is there a relationship between highest year of school completed and socioeconomic index? The two interval/ratio variables are respondent’s highest year of school completed and socioeconomic index. The independent variable is respondent’s highest year of school completed and dependent variable is respondent’s socioeconomic index. The null and alternate hypotheses are Null hypothesis, H0: There is no significant relationship between highest year of school completed and socioeconomic index. Alternate Hypothesis, H1: There is a significant relationship between highest year of school completed and socioeconomic index. The variable highest year of school completed measures respondent’s education in terms of years of schooling completed. The unit of measurement is in years. The variable is a good example for the interval level of measurement, as it has not only a rank but also has meaningful intervals between scale points. The variable socioeconomic index measures respondent socioeconomic index scores reflecting the education, income, and prestige associated with different occupations. There is no unit of measurement for an index value. It is measured in terms of number (or percentage). The variable is a good example for the ratio level of measurement, as it have all the properties of the other three data types (nominal, ordinal and interval), but in addition possess a meaningful zero that represents the absence of the quantity being measured. The average highest year of school completed of respondents is about 13. 15 years and varies from mean by about 3. 04 years. About half of the respondents have highest year of school completed is above 13 years. The range of highest year of school completed is 20 years with minimum and maximum being 0 and 20 years, respectively. A 95% confidence interval for respondent’s highest year of school completed is between 12. 99 to 13. 30 years. Thus, it can be said with 95% confidence that respondent’s highest year of school completed is between 13. 0 to 13. 3 years. The average socioeconomic index of respondents is about 47. 24 and varies from its mean by about 18. 76. About half of the respondents have socioeconomic index above 38. 9. The range of socioeconomic index is 80. 1 with minimum and maximum being 17. 1 and 97. 2, respectively. A 95% confidence interval for respondent’s socioeconomic index is between 46. 26 to 48. 22. Thus, it can be said with 95% confidence that respondent’s socioeconomic index is between 46. 26 to 48. 22. The value of correlation coefficient between highest year of school completed and socioeconomic index is about 0. 585. This indicates a moderately strong positive relationship between highest year of school completed and socioeconomic index. In other words, there appears that as respondent’s highest year of school completed increases, respondent socioeconomic index increases. The regression equation is given by Socioeconomic Index = – 0. 255 + 3. 613(Highest Year of School Completed) The slope regression coefficient is given by 3. 613. This suggests that for every years increase in respondent’s highest year of school completed, increases respondent socioeconomic index by about 3. 613, on average. The intercept regression coefficient is given by – 0. 255 and it has no meaning in given context. The value of coefficient of determination (R2) is 0. 343. This suggests that highest year of school completed explains about 34. 3% variation in respondent socioeconomic index. However, the other 65. 7% variation remains unexplained. Thus, there is moderate effect of highest year of school completed on respondent socioeconomic index. Highest years of school completed significantly predicts respondent socioeconomic index, ? = 0. 59, t(1414) = 27. 15, p . 001. Highest years of school completed also explains a significant proportion of variance in respondent socioeconomic index, R2 = . 34, F(1, 1414) = 737. 24, p . 001. In other words, there is a significant relationship between highest year of school completed and socioeconomic index. We can reject the null hypothesis at the . 05 level of significance as p-value (. 001) is less than . 05. Thus, we can conclude that the research hypothesis is valid for the population of interest and we should generalize to the population level. Since, the sample size is large; therefore, we do not risk any type of error in offering this conclusion. The only concern is that the assumptions (The errors (residuals) are normally distributed, have constant variance and are independent.) related to simple regression analysis is not checked. Research Hypothesis 2 Research Question: Is there a relationship between highest year of school completed and number of hours per day watching television? The two interval/ratio variables are respondent’s highest year of school completed and number of hours per day watching television. The independent variable is respondent’s highest year of school completed and dependent variable is number of hours per day watching television. The null and alternate hypotheses are Null hypothesis, H0: There is no significant relationship between highest year of school completed and number of hours per day watching television. Alternate Hypothesis, H1: There is a significant relationship between highest year of school completed and number of hours per day watching television. The variable highest year of school completed measures respondent’s education in terms of years of schooling completed. The unit of measurement is in years. The variable is a good example for the interval level of measurement, as it has not only a rank but also has meaningful intervals between scale points. The variable number of hours per day watching television measures respondent number of hours per day watching television programs. The unit of measurement is in hours per day. The variable is a good example for the ratio level of measurement, as it have all the properties of the other three data types (nominal, ordinal and interval), but in addition possess a meaningful zero that represents the absence of the quantity being measured. The average highest year of school completed of respondents is about 13. 05 years and varies from mean by about 3. 08 years. About half of the respondents have highest year of school completed is above 12 years. The range of highest year of school completed is 20 years with minimum and maximum being 0 and 20 years, respectively. A 95% confidence interval for respondent’s highest year of school completed is between 12. 89 to 13. 30 years. Thus, it can be said with 95% confidence that respondent’s highest year of school completed is between 12. 9 to 13. 2 years. The average number of hours per day watching television of respondents is about 2. 89 hours and varies from its mean by about 2. 23 hours. About half of the respondent’s number of hours per day watching television is above 2 hours. The range of number of hours per day watching television is 24 hours (may be data error) with minimum and maximum being 0 and 24 hours (may be data error), respectively. A 95% confidence interval for respondent’s number of hours per day watching television is between 2. 78 to 3. 01 hours. Thus, it can be said with 95% confidence that respondent’s number of hours per day watching television is between 2. 8 to 3. 0 hours. The value of correlation coefficient between highest year of school completed and number of hours per day watching television is about -0. 289. This indicates a weak moderate negative relationship between highest year of school completed and number of hours per day watching television. In other words, as respondent’s highest year of school completed increases, number of hours per day watching television decreases. The regression equation is given by Hours per Day Watching TV = 5. 636 – 0. 210(Highest Year of School Completed) The slope of regression coefficients is given by –0. 21. This suggests that for every year increase in respondent’s highest year of school completed, decreases respondent’s number of hours per day watching television by about 0. 21 hours, on average. The intercept of regression coefficients is given by 5. 636, which suggests that individual with no education watches about 5. 6 hours of television each day, on average. The value of coefficient of determination (R2) is 0. 084. This suggests that highest year of school completed only explains about 8. 4% variation in respondent’s number of hours per day watching television. The other 91. 6% variation remains unexplained. Thus, there is very weak effect of highest year of school completed on respondent’s number of hours per day watching television. Highest years of school completed significantly predicts respondent’s number of hours per day watching television, ? = -. 29, t(1483) = -11. 64, p . 001. Highest years of school completed also explains a significant proportion of variance in respondent’s number of hours per day watching television, R2 = . 08, F(1, 1483) = 135. 52, p . 001. In other words, there is a significant relationship between highest year of school completed and number of hours per day watching television. We can reject the null hypothesis at the . 05 level of significance as p-value (. 001) is less than . 05. Thus, we can conclude that the research hypothesis is valid for the population of interest and we should generalize to the population level. Since, the sample size is large; therefore, we do not risk any type of error in offering this conclusion. The only concern is that the assumptions related to simple regression analysis is not checked.