2. A research team took a random sample of 8 observations from a normally distributed random variable Y and observed that yg = 501.2 and s = 4,375.9, where yg was the average of the 8 observations sampled from Y and s was the unbiased estimate of var (Y). A second research team took a random sample of 6 observations from a normally distributed random variable X and observed that x6 = 389.9 and s = 6,710.5, where x6 was the average of the 6 observations sampled from X and s was the unbiased estimate of var(X). Find the 95% var(X) confidence interval for This problem is worth 50 points. var(Y) 3. A research team wishes to test the null hypothesis Ho: p = 0 at a = 0.005 against the alternative H: p>0 using Fisher's transformation of the Pearson product moment correlation coefficient. They have asked their consulting statistician for a sample size n such that =0.10 when p = 0.52. What is this value? This problem is worth 50 points.