Question

Let t0 be a particular value of t. Use Table III in Appendix D to find t0 values such that the following statements are true.

$$\begin{gathered} a.=P(-t_0<t<t_0).95wheredf=10 \\ b.P(t\le -t_{0}ort\ge t_0)wheredf=10 \\ c.P(t\le t_0)=.05wheredf=10 \\ d.P(t\le -t_{0}ort\ge t_0)=.10wheredf=20 \\ e.P(t\le -t_{0}ort\ge t_0)=.01wheredf=5 \end{gathered}$$

Short answer

Answer

1. Not true.
2. Not applicable
3. True
4. True
5. True

Step-by-step solution

Determining the value of t0 when the probability is 0.95 and degrees of freedom is 10

a.

The two-tail test is applicable in this case. With the help of MS Excel, the exact value of t0 can be found to be 0.064298 when the degrees of freedom is 10. This shows that statement is not true. The value of t0 is very less than the values of t (taking reference from Appendix D).

Determining the value of t0 when the probability is unknown and degrees of freedom is 10

In this subpart, the solution cannot be found as the value of the probability is not there.The value of the probability is required in this subpart to denote the value of the t0.

Determining the value of t0 when the probability is 0.05 and degrees of freedom is 10

c.

In this subpart, the one-tail test is applicable. With the help of MS Excel, the exact value of t0 can be found to be 1.81246 when the degrees of freedom is 10. This shows that statement is true. The value of t0 is greater than the value of t at t_.050, which is 1.725 (taking reference from Appendix D).

 Step 4: Determining the value of t0 when the probability is 0.10 and degrees of freedom is 20

e.

In this subpart, the two-tail test is applicable, and so, with the help of MS Excel, the exact value of t0 can be found to be 1.72472 when the degrees of freedom is 20. This shows that statement is true as the value of t0 is greater than the value of t at t_.100, which is 1.325 (taking reference from Appendix D).

Determining the value of t0 when the probability is 0.01 and degrees of freedom is 5

f.

In this subpart, the two-tail test is applicable, and so, with the help of MS Excel, the exact value of t0 can be found to be 4.0321 when the degrees of freedom is 5. This shows that statement is true as the value of t0 is greater than the value of t at t_.010, which is 3.365 (taking reference from Appendix D).