A researcher is studying the effects of choices made by students entering middle school on future SAT outcomes. The researcher records the math course that the student enrolls in upon entering the sixth grade. The researcher uses SAT data for the same group of students, grouping students by college readiness. The data is displayed below.
| College Ready | Likely College Ready | Not College Ready | |
|---|---|---|---|
| Grade-level | 26 | 82 | 114 |
| Honors | 43 | 79 | 94 |
| Accelerated | 8 | 18 | 17 |
Do the data suggest that sixth grade math enrollment and SAT college readiness are related? Use a 5% level of significance.
a) Write out a null and alternate hypothesis.
b) Calculate the chi-squared test statistic:
c) What is the degree of freedom?
d) Calculate the p-value:
e) Write a conclusion in context.
f) What is the expected count for a student who entered sixth grade in an honors math class who obtained "college ready" designation based on the SAT?
g) What is the contribution to the chi-squared test statistic for this cell (from part (f))?