Do students tend to improve their math SAT scores the second time they take the test? A random sample of four students who took the test twice received the following scores. The difference should be recorded as (second score - first score) so that the differences are all positive. (You may not need all of the following symbols, but please type "mu" for M, "sigma" for o, "neq" for #, and don't include extraneous spaces). Student 1 2 3 4 First Score 440 520 710 600 Second Score 490 600 720 630 a. State the null hypothesis. b. State the alternative hypothesis. c. What p-value do you get when you perform the appropriate hypothesis test? Round your answer to 3 decimal places. d. Should the null hypothesis be rejected at the a = .05 level of significance? Type "reject" or "do not reject" e. Write a proper conclusion. (This question will be graded separately by the instructor, and will likely be marked incorrect by Canvas). There is (type "sufficient" or "insufficient") evidence at the a = .05 level of significance to conclude that for students taking the SAT two times f. What would it mean for the researcher to make a Type II error? (This question will be graded separately by the instructor, and will likely be marked incorrect by Canvas). The researcher would conclude that for students taking the SAT two times