According to the American Psychiatric Association, posttraumatic stress disorder (PTSD) is a common ...

According to the American Psychiatric Association, posttraumatic stress disorder (PTSD) is a common psychological consequence of traumatic events that involve a threat to life in physical integrity. Researchers studied PTSD patients that were imprisoned for political reasons in East Germany during the Cold War. They randomly and independently selected 32 former prisoners diagnosed with chronic PTSD and 20 former prisoners that were diagnosed with PTSD after release from prison but had since recovered (remited). Their ages at arrest were recorded and yielded the following summary statistics.

Chronic

Remitted

a) Is it appropriate to assume there to be no difference between the standard deviations of ages of former prisoners with chronic PTSD and those with remitted PTSD? Perform a hypothesis test at the 10% level to make your decision.

b) At the 5% significance level, is there sufficient evidence to conclude that a difference exists in the mean age at arrest of East German prisoners with chronic PTSD and remitted PTSD? Perform a hypothesis test using the critical value method. Choose the appropriate procedure (pooled or non-pooled?) based on your conclusion for the last question. 

c) Find the P-value of the above hypothesis test.

d)Explain why you chose to use the above procedure (pooled t-test / nonpooled t-test), and why it’s appropriate to use it. Are there any conditions that needs to be confirmed via further study?