In the article "Sleep Apnea in Adults With Traumatic Brain Injury: A Preliminary Investigation" (Archives of Physical Medicine and Rehabilitation, Vol. 82, Issue 3, pp. 316321), J. Webster et al, investigated sleep-related breathing disorders in adults with traumatic brain injuries (TBI). The respiratory disturbance index (RDI), which is the number of apneic and hypopneic episodes per hour of sleep, was used as a measure of severity of sleep apnea. An RDI of 5 or more indicates sleep-related breathing disturbances. The RDIs for the females and males in the study are as follows.

Use the technology of your choice to answer the following questions. Explain your answers.

a. If you had to choose between the use of pooled$t$-procedures and nonpooled $t$-procedures here, which would you choose?

b. Is it reasonable to use the type of procedure that you selected in part (a)?

Given in the question that, In the article "Sleep Apnea in Adults With Traumatic Brain Injury: A Preliminary Investigation" (Archives of Physical Medicine and Rehabilitation, Vol. 82, Issue 3, pp. 316321), J. Webster et al, investigated sleep-related breathing disorders in adults with traumatic brain injuries (TBI). The respiratory disturbance index (RDI), which is the number of apneic and hypopneic episodes per hour of sleep, was used as a measure of severity of sleep apnea. An RDI of 5 or more indicates sleep-related breathing disturbances. The RDIs for the females and males in the study are as follows.

we need to find that which one we choose pooled $t$-procedures or nonpooled $t$-procedures.

Consider the table,

Because the two sample standard deviations from two populations are significantly different and sample sizes are unequal, the non-pooled $t-$procedure is utilised.

Given in the question that, In the article "Sleep Apnea in Adults With Traumatic Brain Injury: A Preliminary Investigation" (Archives of Physical Medicine and Rehabilitation, Vol. 82, Issue 3, pp. 316321), J. Webster et al, investigated sleep-related breathing disorders in adults with traumatic brain injuries (TBI). The respiratory disturbance index (RDI), which is the number of apneic and hypopneic episodes per hour of sleep, was used as a measure of severity of sleep apnea. An RDI of 5 or more indicates sleep-related breathing disturbances. The RDIs for the females and males in the study are as follows.

we need to verify that whether it is reasonable to use the type of procedure that you selected in part (a)

The graph for the above are shown below,

and

In light of the foregoing normal plots, it is not appropriate to employ the non pooled$t$-procedure because the normal plot for male data indicates the presence of outliers. As a result, the male population is out of the ordinary.