1. Suppose you are working on a research report that investigates racial differences in home ownership in the US. You utilized the General Social Survey, 2014 of 1,054 Americans to assess home ownership among White (N=882) and Black adults (N=172). You found that 619 White adults and 68 Black adults in your sample owned homes.
a. Calculate the proportion of White and Black adults who own homes. Construct the 95% confidence interval for the proportion of home ownership among both White and Black adults (i.e., estimate the confidence interval separately for both White and Black adults). [2+5= 7 points]
b. Construct the 99% confidence interval for the proportion of home ownership among both White and Black adults (i.e., estimate the confidence interval separately for both White and Black adults) [5 points].
c. Which of the confidence interval (i.e., 95% or 99% confidence interval) would you prefer to use for your report? Explain why [3 points].
2. You know from sociological theories that women experience systemic disadvantages in the labor market. Such discrimination could lead to gender differences in income. You are interested in examining the possibility of income differences between men and women. You draw from the General Social Survey, 2014 to produce the descriptive statistics presented below.
Gender N Minimum Maximum Mean Std. Deviation
Men 456 500 160000 56077.30 43502.64
Women 456 500 160000 36021.38 29980.13
a. State the null hypothesis [1 point].
b. State the research hypothesis [1 point].
c. Would you set up your hypothesis as a directional hypothesis? In other words, would you set it up as a one-tailed or a two-tailed test? [2 points]
d. Identify the test statistic and provide the formula [2 points].
e. Setting alpha of .05, what do you conclude based on the test statistic (=8.11; p-value=0.000) you calculated? Are you able to reject the null hypothesis? Why or why not? Provide a detailed explanation. [5+2+2=9 points].