1. To see if students tend to improve their SAT Mathematics (SAT-M) score the second time they take the test, a random sample of 5 students who took the test twice was selected. The students received the following scores. test first 500 530 600 440 710 second 580 610 570 410 710 Assume that first and second SAT-M scores and their differences for the population of all students are normally distributed. Perform the appropriate statistical test of hypothesis at the 5% level to determine if students tend to improve their SAT-M score the second time they take the test. Clearly identify the hypothesis you are testing, report the value of the test statistic and the p-value or critical value that you are using to make your decision, and state your conclusion in the context of the