8. Question: Do students tend to improve their SAT Mathematics (SAT-M) score the second time they take the test? A random sample of four students who took the test twice received the following scores: Student 1 2 3 4 First score 450 520 720 600 Second score 440 600 720 630 (a) What is a 90% confidence interval for u , the mean change in SAT-M score? (b) Suppose we do not believe that students tend to improve their SAT-M score the second time they take the test. Based on the confidence interval previously calculated, we wish to test Ho : u = 0 versus Ha : p # 0 at the 5% significance level. Determine which of the following statements is true: i. We cannot make a decision since the confidence interval is so wide. ii. We cannot make a decision since the confidence level we used to calculate the confidence interval is 90%, and we would need a 95% confidence interval. iii. We accept Ho since the value 0 falls in the 90% confidence interval and would therefore also fall in the 95% confidence interval. iv. We reject Ho since the value 0 falls in the 90% confidence interval