Question

A researcher has developed a regression model from fourteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two- tailed test and α = 0.01. The critical table t value is _______.

Answer 1

The critical table t-value for the two-tailed test with α = 0.01 and 14 pairs of data points is approximately 2.681.

Step-by-step explanation:

The critical table t value for a two-tailed test with α = 0.01 and fourteen pairs of data points (n=14) can be determined by the degrees of freedom, which in this case is n-2 = 14-2 = 12.

To find this critical value, one would look at the t-distribution table for the specified degrees of freedom and the significance level.

Although the specific value is not provided here, you would locate the value corresponding to the 0.01 level (two-tailed) across the row for df = 12.

If the calculated t value from the regression analysis is greater than the critical value from the table, then the null hypothesis (that the slope is not significantly different from zero) is rejected.

Conversely, if the calculated t value is less than the critical value, you would fail to reject the null hypothesis.

The researcher wants to test if the slope is significantly different from zero in his regression model. He uses a two-tailed test with α = 0.01.

To find the critical table t value, we need to determine the degrees of freedom. Since the researcher has developed the regression model from fourteen pairs of data points, the degrees of freedom will be 14 - 2 = 12.

Using a t-table, the critical t-value for α = 0.01 and 12 degrees of freedom is approximately 2.681.

So, the critical t-value is 2.681.