A research team took a random sample of 4 observations from a normally distributed random variable Y and observed that y4 = 18.2 and sy = 82.4, where y4 was the average of the 4 observations sampled from Y and sy was the unbiased estimate of var (Y ) (i.e., the divisor in the variance was n -1). A second research team took a random sample of 6 observations from a normally distributed. random variable X and observed that X = 34.7 and sy = 105.2, where X6 was the average of the 6 observations sampled from X and sy was the unbiased estimate of var (X) (i.e., the divisor in the variance was n -1). Test the null hypothesis Ho: E(X) = E(Y) against the alternative H, : E (X) # E(Y ) at the 0.10, 0.05, and 0.01 levels of significance using the pooled variance t-test. This problem is worth 50 points