Chapter 2

Question 0

What are statistics used for?

Answer 0

To make inferences about unknown population parameters.

Question 1

What are inferences?

Answer 1

estimates or decisions

Question 2

Why are all statistics random variables?

Answer 2

Because all statistics are functions of random variables observed in a sample

Question 3

What is the test concerning B_1, the slope of the regression line.

Answer 3

H_0: B_1 = 0 (there is no linear association between Y and X)
H_1: B_0 not equal 0

Question 4

Why is the probability distribution of Y identical when B_1 = 0?

Answer 4

Since (in the model) all probability distributions of Y are normal with constant variance

Question 5

What is the sampling distribution of b_1?

Answer 5

The sampling distribution of b_1 refers to the different values of b_1 that would be obtained with repeated sampling when the levels of the predictor variable X are held constant from sample to sample.

Question 6

What is E[b_1] and V[b_1] for a normal regression model where the sampling distribution of b_1 is normal, with mean and variance…

Answer 6

E[b_1]= B_1
V[b_1]= ((sigma)^2)/ Sum(X_i - Xbar)^2

Question 7

T/F: b_1 is not a linear combination of the Y_i

Answer 7

F: “The normality of the sampling distribution of b_1 follows at once from the fact that b_1 is a linear combination of the Y_i.