Final answer:
The value of the test statistic for the simple linear regression, given b1 = 3.05 and se(b1) = 1.40, is calculated to be 2.18. This statistic is used to test the significance of the linear relationship between the two variables.
Step-by-step explanation:
To calculate the value of the test statistic in a simple linear regression, we use the estimated coefficient (b1) and its standard error (se(b1)). The hypothesis is testing if there is a significant linear relationship between the independent variable and the dependent variable, with the null hypothesis H0: β1 = 0, and the alternative hypothesis HA: β1 ≠ 0.
The formula for the test statistic is:
t = (b1 - β0) / se(b1)
Where β0 is the hypothesized value of the coefficient under the null hypothesis. In this case, β0 is 0.
Therefore, the test statistic is:
t = (3.05 - 0) / 1.40
t = 3.05 / 1.40
t = 2.18
This is the value of the test statistic that will be compared to the t-distribution with n-1 degrees of freedom to determine whether to reject or fail to reject the null hypothesis.