Question

The statistical model for simple linear regression is written as μ_y = β0 + β1*x, where μ_y represents the mean of a Normally distributed response variable and x represents the explanatory variable. The parameters β₀ and β₁ are estimated, giving the linear regression model defined by μ_y = 70 + 10*x , with standard deviation σ = 5.

(multiple choice question)

What is the distribution of the test statistic used to test the null hypothesis H₀ : β₁ = 0 against the alternative hypothesis H_a : β₁ > 0 ? (note: n is the sample size)

a.) N (0,1)

b.) N (0,2)

c.) t (n-1)

d.) t (n-2)

Answer 1

To test

Ho : 1 = 0

H1 : 1 > 0

the test statistic is given by

where b1 is slope of equation

Sb1 : standard error of slope

1 : Hypothesized value of slope

here statistic t follows t distribution with (n-k-1) degrees of freedom

since we have one independent variable X, k =1

therefore  t follows t distribution with (n-2) degrees of freedom

option d t(n-2) is correct