Proper nutrition is essential for aircraft pilots, given the demands of their job.
Previous studies have indicated that United States Air Force pilots do not
regularly eat breakfast, and thus may have low blood glucose levels after fasting
at night. To investigate the potential for danger, 8 pilots were selected for study
in flight simulators. Each pilot participated in two trials and they tried a different
drink, either Drink A (high carbohydrate) or Drink B (low carbohydrate) in each
trial. The order in which the drinks were tried was determined at random. The
second trial was conducted 2 days after the first trial, so that any effects of the
first drink were eliminated. After consuming one of the drinks, the pilots were
subjected to a variety of attitude recovery tasks. (An attitude recovery task is one
where the pilot must return to wings-level flight.) The duration of self-illusory
motion (time between wings-level flight and the pilot to "feel" he or she has
returned to wings-level flight) are shown in the table below. Graphical displays
of the data indicate that it is reasonable to assume that the two "felt recovery
time" distributions are approximately normal. $$\begin{array}{l}
\text { Duration of self-illusory motion (sec) }\
\begin{array} { l c c c c c c c c }
\text { Pilot } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\text { Drink A } & 31 & 27 & 29 & 33 & 23 & 25 & 23 & 24 \
\text { Drink B } & 34 & 23 & 29 & 20 & 24 & 26 & 26 & 27
\end{array}
\end{array}$$ Do these data provide convincing evidence that the mean self-illusory motion time
differs for the two drinks? Provide appropriate statistical justification for your
conclusion.

Question

Proper nutrition is essential for aircraft pilots, given the demands of their job.
Previous studies have indicated that United States Air Force pilots do not
regularly eat breakfast, and thus may have low blood glucose levels after fasting
at night. To investigate the potential for danger, 8 pilots were selected for study
in flight simulators. Each pilot participated in two trials and they tried a different
drink, either Drink A (high carbohydrate) or Drink B (low carbohydrate) in each
trial. The order in which the drinks were tried was determined at random. The
second trial was conducted 2 days after the first trial, so that any effects of the
first drink were eliminated. After consuming one of the drinks, the pilots were
subjected to a variety of attitude recovery tasks. (An attitude recovery task is one
where the pilot must return to wings-level flight.) The duration of self-illusory
motion (time between wings-level flight and the pilot to "feel" he or she has
returned to wings-level flight) are shown in the table below. Graphical displays
of the data indicate that it is reasonable to assume that the two "felt recovery
time" distributions are approximately normal. $$\begin{array}{l}
\text { Duration of self-illusory motion (sec) }\
\begin{array} { l c c c c c c c c } 
\text { Pilot } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\text { Drink A } & 31 & 27 & 29 & 33 & 23 & 25 & 23 & 24 \
\text { Drink B } & 34 & 23 & 29 & 20 & 24 & 26 & 26 & 27
\end{array}
\end{array}$$ Do these data provide convincing evidence that the mean self-illusory motion time
differs for the two drinks? Provide appropriate statistical justification for your
conclusion.

Quizplus · Accepted Answer

The Answer is Let

\mu _ { d }

represent the mean difference (A - B) in felt recovery time to wings level for treatments A and B

\begin{array} { l } H _ { 0 } : \mu _ { d } = 0 \H _ { a } : \mu _ { d } eq 0\end{array}

The problem states that the assumptions for the

t

-procedure are met.

\begin{array} { l } t = \frac { \bar { d } - 0 } { \sqrt { \frac { s _ { d } ^ { 2 } } { n _ { d } } } } = \frac { 0.75 - 0 } { \sqrt { \frac { 5.471 ^ { 2 } } { 8 } } } = 0.3878 \P - ext { value } = 0.71 , d f = 7\end{array}

Since the

P

-value is very large, we cannot reject the null hypothesis. There is not sufficient evidence of a difference in mean felt recovery times to wings level between drinks

A

and

B

.

Proper Nutrition Is Essential for Aircraft Pilots, Given the Demands