As an educational researcher, would like to know whether high school student perceptions about mathematical utility changed between their freshman and senior year. Each respondent is asked the same series of questions about the utility of mathematics in their future during their freshman and senior year. These questions are combined to form one variable of mathematical utility; higher values indicate higher levels of mathematical utility.

Using the High School Longitudinal Survey. Note the relevant statistics, comment on meaningfulness, and include your relevant SPSS output.

1. Write an analysis of your t test results for the research scenario and include your research questions and the SPSS syntax and output. Do not forget to evaluate if the t test assumptions are met, justify the selection of type of t test, and report the effect size. Based on your results, provide an explanation of what the implications of social change might be.