Answer Happy

Let X and Y denote weight in grams of an apple, respectively taken from two different orchards. Assume that X is normally distributed with mean µx and variance of, and Y is normally distributed with mean μy and variance o}. A random sample of size n = 16 is drawn for X, and a random sample of size m = 13 is drawn for Y from the respective orchards. (i) (b) Assume that a = o?, give the test statistic and critical region for testing the null hypothesis Ho: x = Hy against the alternative hypothesis H₁: Mx > Hy at the 0.05 level of significance. (ii) It is given that the sample mean and sample variance are x = 415.16 and s= 1356.75 for X, and y = 347.40 and s = 692.21 for Y, respectively. Using part (i), calculate the value of the test statistic and state your conclusion. Let Y be a binomial random variable with number of trials, n, and probability of success, p. Using Chebyshev's inequality, show that Y/n converges in probability to p as n → ∞.