Two-sample t-tests Investigating Minority Enrollment 
Statistical Topic:
How one tests two sample means is determined by whether the two samples are independent or dependent.  If one sample is dependent to another, there is some relationship between the two samples such as the same subject used for both samples.  Examples of these types of samples are differences in time and pre-test and post-test situations.  Two samples are independent if there is no relationship between data values in one sample to data values in another sample such as a group of female students compared to a group of male student for test scores.  T-tests are a type inferential analyses (experimental design) that allow us to answer a research question about differences in means for two samples. We need data description to find the important descriptive statistics such as the mean and standard deviation for each sample and the histograms for each sample are used to determine if our sample is approximately normally distributed.
Student Issue:
Is there an increase in minority enrollment from 1986 to 1996?  Do southern states have a different percent enrollment of minorities than do northern states? 
Data Sets:
 Consult Table 45. Enrollment in public elementary and secondary schools, by race or ethnicity and state. from NCES (National Center for Education Statistics)'s publication 1998 Digest of Education Statistics.
Goal of Data Analysis Lab:
Using the two different types of t-test, answer the following two research questions: 
  1. Is there a mean difference in minority enrollment between 1986 and 1996?
  2. Is there a mean difference in minority enrollment between 1996 northern and 1996 southern states?
Statistical Techniques:
  1. Determine which of the two research questions tests differences in dependent means and in independent means.
  2. Working with your partner, input the data and define the variable for the states selected from Table 45 into the a data editor such as SPSS or Excel (those marked N for north and S for south).  Label the first column as state, the second as N/S (for northern or southern), the third as white86 and the fourth as white96.
  3. You have inputted two variable, white86 and white96 that represent the percent enrollment of elementary and secondary schools which are white.  You need to recode the white86 and white96 to new variables called minor86 and minor96 which meassure the percent minority by selecting TRANSFORM/COMPUTE from the menu bar.  The first target variable is minor 86 and  the numeric expression is 100-white86.  For the second variable, the second target variable is minor96 and the the numeric expression is 100-white96.  These computed variables are located to the right of the original data set and are the variables that measure minority enrollment. 
  4. Run the appropriate analysis for each research question and paste results into Microsoft Word. 
  5. Determine if the test assumptions for t-tests have been meet by comparing histograms for each sample? Again paste into Word. Each partner printout the results and save to disk.
  6. Complete the five steps of hypothesis testing for each research question.  Write a summary of your results.
Social Commentary:
  1. How does an increase or decrease in minority enrollment affect all students in schools?
  2. Do you know of incidences in which racial biases and prejudices affected learning?