Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. In a sample of 200 such students, the average of the differences was 33 points with a standard deviation of 28.2843 points.

Test the claim that retaking the SAT increases the score on average by more than 30 points.

(a) Find the test statistic.

(b) Test the claim at the 0.10 significance level.

Critical value:

Is there sufficient data to support the claim?
Yes
No

(c) Test the claim at the 0.01 significance level.

Critical value:

Is there sufficient data to support the claim?
Yes
No