Statistical Inference: A Short Course

Exercises

1. Suppose a population of size N = 5 consists of the X values: 2, 4, 6, 8, 10. If we take all possible samples of size n = 2 without replacement, how many samples will we obtain? Find the sampling distribution of the mean. Graph its probability mass function. Next, find the following:

a. μ and σ

b. and

c. The standard error of the mean

d. Verify that

2. Let the population variable X be N(50, 10). What is the probability that the mean of a sample of size n = 25 will differ from μ by less than four units? Resolve this problem for n = 50 and for n = 100. What can we conclude?

3. Let the population variable X be N(100, 10). What is the probability that the mean of a sample of size n = 25 will be within ± 5 units of μ? Resolve this problem for σ = 16. What can we conclude?

4. Suppose a population variable X consists of the values 1, 2, 3, 4, 5, 6. For samples of size n = 3 taken without replacement, determine the sampling distribution of the mean. Find and . What is the ...