Question

The regression equation is Ŷ = 29.29 − 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the critical value to test whether the slope is different from zero at the 0.01 significance level?

a.t = ±3.707
b.t = +3.355
c.z = +2.326
d.z = ±2.576

Answer 1

The critical value at the 0.01 significance level for a t-distribution with 6 degrees of freedom (from a sample size of 8) is approximately ±3.707.

Step-by-step explanation:

To determine the critical value to test whether the slope is different from zero at the 0.01 significance level, we need to use a t-distribution because the sample size is small (n=8) and we likely do not know the population standard deviation.

Since the sample size is 8, to find the degrees of freedom for our t-test, we subtract 2, giving us df = n - 2 = 6. Looking up the critical value in a t-distribution table for a two-tailed test at the 0.01 significance level with 6 degrees of freedom, we find that the critical t-value is approximately ±3.707.

Therefore, the answer is:

• a. t = ±3.707