A publishing company has developed a study guide (reference book) for GRE Math test. They want to test if this reference book does help students perform better on the test. The company recruited a random sample of 10 students who are planning to take this test and let them use the new reference book. Their scores are listed below. Test the null hypothesis that the 10 students' mean score is not different from the national average (at a significance level of .05) by answering the following questions. The national statistics indicates that the average score for the population is 68.5.

Scores:64,6992,77,71,99,82,74,69,88

(1)Set up hypotheses (2 pts):

(2) What is the df and thecritical value for this test? (2 pts):

(3) What is the standard error for this test? (2 pts)

(4) What is the t_observed for this test? (2 pts)

(5) Provide the decision and the interpretation (2 pts)