Question: Hypothetical data, based on Gee et.al., Self-Reported Discrimination and Mental Health Status Among African Descendants, Mexican Americans, and Other Latinos in the New Hampshire REACH 2010 Initiative, AJPH Oct 2006). A study was conducted to examine the association between discriminatory experiences and mental health in a minority population. A sample of 200 Blacks and Mexican Americans was interviewed and asked about perceived discrimination relative to their goals in life, ‘Do you feel that racial discrimination diminishes your ability to achieve your goals fully’. Mental health was measured through the MCS, a measure of overall psychological well- being where higher scores indicate better mental health.

Data from this sample are saved in the .csv file accompanying this midterm. Variables in the data set are: 1) an id number, ranging from 1 to 200; 2) respondent sex, coded as 1 for females and 0 for males; 3) ethnicity, coded 1 for Black and 2 for Mexican American; 4) age, in years; 5) goals discrimination, coded as 1 for those who responded that discrimination diminishes their ability to achieve goals and 0 for those who did not report goals discrimination; and 6) the MCS mental health score, ranging from 20 to 73 in this sample with higher values indicating better mental health.

Our primary study question is whether those who perceive discrimination have poorer mental health than those who do not perceive discrimination.

(A) (20 points) What is the level of perceived discrimination among these minority groups? As a preliminary analysis, find the percent of Blacks perceiving discrimination, and the percent of Mexican Americans perceiving discrimination. Find and interpret 95% confidence intervals for each of these two percentages.

(B) (15 points) Do Blacks and Mexican Americans differ on mean MCS mental health score? As a second preliminary analysis, find the mean MCS mental health score for Blacks, and the mean MCS mental health score for Mexican Americans. Compare these means through an appropriate statistical procedure – find and interpret a p-value for this comparison.

(C) (15 points) Do minorities who perceive discrimination have poorer mental health than those who do not perceive discrimination? Compare the mean MCS mental health score between those who perceive discrimination vs. those who do not perceive discrimination through an appropriate statistical procedure – find and interpret a p-value for this comparison. Regardless of your finding in 2B, perform this analysis on the combined Black and Mexican American sample.