Ten healthy adult subjects were asked to walk on a treadmill while connected to monitors. One of two kinds of disturbances was applied during the walk, and the number of steps until adaptation was recorded. Each subject experienced both kinds of disturbance, in random order. Here are the summary data for these 10 subjects:
?
$$\begin{array} { | l | l | l | l | l | }
\hline & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \
\hline \text { Disturbance A } & 10 & 7.320 & 2.10016 & 0.66413 \
\hline \text { Disturbance B } & 10 & 5.170 & 1.86073 & 0.58842 \
\hline \text { Difference A-B } & 10 & 2.150 & 2.68711 & 0.84974 \
\hline
\end{array}$$ A test is conducted to test whether there is significant evidence of a different mean adaptation time (in steps) for the two disturbances. What is the test statistic for the appropriate test of hypothesis?

Question

Ten healthy adult subjects were asked to walk on a treadmill while connected to monitors. One of two kinds of disturbances was applied during the walk, and the number of steps until adaptation was recorded. Each subject experienced both kinds of disturbance, in random order. Here are the summary data for these 10 subjects:
?
$$\begin{array} { | l | l | l | l | l | } 
\hline & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \
\hline \text { Disturbance A } & 10 & 7.320 & 2.10016 & 0.66413 \
\hline \text { Disturbance B } & 10 & 5.170 & 1.86073 & 0.58842 \
\hline \text { Difference A-B } & 10 & 2.150 & 2.68711 & 0.84974 \
\hline
\end{array}$$ A test is conducted to test whether there is significant evidence of a different mean adaptation time (in steps) for the two disturbances. What is the test statistic for the appropriate test of hypothesis?

Quizplus · Accepted Answer

The appropriate test of hypothesis is a paired t-test, since the same subjects are being compared under two different conditions. The test statistic for a paired t-test is:t = (mean difference) / (standard error of the mean difference)In this case, the mean difference is 2.150 and the standard error of the mean difference is 0.84974. Therefore, the test statistic is:t = 2.150 / 0.84974 = 2.53

Ten Healthy Adult Subjects Were Asked to Walk on a Treadmill