Econometrics- Explain the central limit theorem in the context
12/26/2014 14:50
1. In a population it is known that µx = 50 and sx2 = 36. Suppose that the following random samples were selected from this population. Use the central limit theorem to answer the following questions. Note that this question is about X-, while the previous homework (Problem 1) asked about X.
a. In a random sample of size n = 100, find Pr(X-< 51)
b. In a random sample of size n = 81, find Pr(49<X-<51)
c. Explain the central limit theorem in the context of the current problem, and indicate how it was useful in finding these probabilities.
2. Find the critical Z values in each of the following cases:
a. α = 0.05 (one-tailed test)
b. α = 0.05 (two-tailed test)
c. α = 0.10 (one-tailed test)
d. α = 0.01 (two-tailed test)