2. A research team took a random sample of 7 observations from a normally distributed random variable Y and observed that yˉ​7​=48.6 and sY2​=27.4, where yˉ​7​ was the average of the 7 observations sampled from Y and sY2​ was the unbiased estimate of Var(Y). A second research team took a random sample of 5 observations from a normally distributed random variable X and observed that xˉ5​=28.0 and sX2​=32.7, where xˉ5​ was the average of the 5 observations sampled from X and sX2​ was the unbiased estimate of Var(X) (a) Test the null hypothesis H0​:E(X)=E(Y) against the alternative H1​:E(X)=E(Y) at the 0.10,0.05 and 0.01 levels of significance using the pooled variance t-test. (b) Show the 95% confidence interval for E(X)−E(Y).