Question

1. (+1 each) State whether each of the following is always true (T) or not always true (a) If X1, X,X are drawn from the same population distribution, then X is ,Xn are not an unbiased estimator of the population mean μ, even if X1, X2, independent (b) Increasing the level a of a hypothesis test decreases the probability of rejecting the nul hypothesis. (c) A null hypothesis with a p-value of 0.02 is rejected at the 0.01 level. (e) The Law of Large Numbers states that the sample mean X of a large number of observations, drawn independently from the same population, is approximately normally distributed around the population mean (f) If the hypothesis that = 2 is rejected at the α = 0.01 level in favor of the hypothesis that ơi > 2, then the hypothesis that as 0.01 level 1. = 1 is rejected at the infavor of the hypothesis that

Answer 1

a) False. We need X1,X2,....Xn to be independent

b) False . Decreasing the level of alpha reduces the probability of rejecting the null hypothesis

c) False. Since the p-value of 0.02 > 0.01 the significance level, we fail to reject the null hypothesis. (Null hypothesis is only rejected when the p-value of the test< significance level considered)

d) True (from the central limit theorem)