Question

Mandate Perceptions. L. Grossback et al. examined mandate perceptions and their causes in the paper "Comparing Competing Theories on the Causes of Mandate Perceptions" (American Journal of Political Science, Vol. 49, Issue 2, pp.406−419406−419). Following are data on the percentage of members in each chamber of Congress who reacted to mandates in various years.
Use the technology of your choice to answer the following questions. Explain your answers.
a. if you have to choose between the use of pooled t -procedures and non-pooled t -procedures here, which would you choose?
b. Is it reasonable to use the type of procedure that you sclected in part (a)?

Short answer

(a) Nonpooled t-test is appropriate. On comparing the standard deviations, $s_{house}=11.13\ne s_{count}=8.29$. So nonpooled t- test is recommended.

(b) Yes, it is reasonable to use the nonpooled t-test because the normal probability plot shows the normality of each of the members.

Step-by-step solution

Part (a) Step 1. Given Information.

The data on the percentage of members in each chamber of Congress who reacted to mandates in various years.

Part (a) Step 2. MINITAB procedure.

By usinng MINITAB,

Part (a) Step 3. Explanation.

Nonpooled t-test is appropriate. On comparing the standard deviations,$s_{house}=11.13\ne s_{count}=8.29$ . So nonpooled t- test is recommended.

Part (b) Step 1. Draw the probability plot of senate and house.

The probability plot of senate is:

And the probability plot of house iss:

Part (b) Step 2. Explanation.

Yes, it is reasonable to use the nonpooled t-test because the normal probability plot shows the normality of each of the members.