$$\text { Determine the value of } \alpha \text { as shown in the figure below, if the degrees of freedom were } 7 \text { and }$$ 9.

A) 0.01
B) 0.025
C) 0.05
D) 0.1

Question

$$\text { Determine the value of } \alpha \text { as shown in the figure below, if the degrees of freedom were } 7 \text { and }$$ 9.

A) 0.01 
B) 0.025 
C) 0.05 
D) 0.1

Quizplus · Accepted Answer

The figure shown is the t-distribution table. Degrees of freedom of 7 corresponds to the row with heading 6 and degrees of freedom of 9 corresponds to the row with heading 8. Since we want to find the value of $\alpha$, we need to look at the top row to see the different levels of significance.

At the 5% level of significance, corresponding to the column with heading 0.05, the value of t for 6 degrees of freedom is 1.943, and the value for 8 degrees of freedom is 1.860.

Using the fact that $t_{\alpha/2}(df) = -t_{1-\alpha/2}(df)$ for a two-tailed test, we can set up an equation:

$t_{0.025}(7) = -t_{0.025}(9)$

$1.943 = -1.860$

This is not true, so we need to try a different value of $\alpha$.

At the 2.5% level of significance, corresponding to the column with heading 0.025, the value of t for 6 degrees of freedom is 2.447, and the value for 8 degrees of freedom is 2.306.

Setting up the equation again:

$t_{0.0125}(7) = -t_{0.0125}(9)$

$2.447 = -2.306$

This is true, so $\alpha$ equals 0.025. Therefore, the answer is B.