here's my question

4. Blood pressure consists of two numbers, the systolic (upper) number and the diastolic (lower) number. Medical researches want to understand the difference in magnitude between a person's systolic and diastolic blood pressure. For a random person selected from the population, let X be their systolic pressure, and let Y be the diastolic pressure. We randomly sample the blood pressure of n peeple, (X1, Y1), . . . , (Xn, Y\"). Let D = X Y and D; = X; Y;, i = 1, . . . ,n. Suppose we can accurater model D as a normal random variable, but whose mean up and variance 0% are unknown. (a) (6 points) Suppose we take n = 7 samples and nd Subject X1; 12 1 111 59 2 121 78 3 136 91 4 125 63 5 114 83 6 118 81 7 142 93. Find a two-sided 95% condence interval for [1.1). (b) (6 points) Old heath data suggests up = 40. The researchers want to try to establish a new claim that the average difference between systolic and diastolic pressure has increased in recent years. The researchers take n = 17 random samples. Use the test statistic D - 40 SD/ V17 to form a test with significance level a = 0.05. Justify your