It is claimed that college-bound seniors tend to do a bit better on Math than on Verbal SATs. We would like to see if this is true for the larger population of students at a university, based on a sample of several hundred college students who took part in a survey.
a. Does the claim that college-bound seniors do better on Math than on Verbal SATs constitute the null hypothesis or the alternative?
b. Use software to access the student survey data, and perform the appropriate test. Report the mean of sampled differences, the standardized mean, and the P-value.
c. Do the data support the abovementioned claim?
d. Use software to obtain a 95% confidence interval for the mean of differences, Math minus Verbal.
e. Which of these are plausible values for the mean of differences, Math minus Verbal -20, -10, 0, 10, or 20? Tables
f. Explain why we should not generalize about the difference between Math and Verbal scores to all universities, based on a sample of students from a particular university.
g. This exercise considered a quantitative variable, score, compared for two kinds of test (Math or Verbal). What types of variables would be involved if we were interested in the relationship between Math and Verbal scores, so that we could predict a student's Math score, given his or her Verbal score?