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 data for these 10 subjects:
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$$\begin{array} { | l | l | }
\hline \text { Disturbance A } & \text { Disturbance B } \
\hline 11.5 & 4.5 \
\hline 8.3 & 3.4 \
\hline 7.4 & 5.5 \
\hline 5.4 & 3.3 \
\hline 8.2 & 7.2 \
\hline 8.8 & 4.7 \
\hline 4.5 & 4.1 \
\hline 6.8 & 9.4 \
\hline 7.5 & 5.2 \
\hline 4.8 & 4.4 \
\hline
\end{array}$$ What are the null and alternative hypotheses to test whether there is significant evidence of a different mean adaptation time (in steps) for the two disturbances?

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 data for these 10 subjects:
?
?
$$\begin{array} { | l | l | } 
\hline \text { Disturbance A } & \text { Disturbance B } \
\hline 11.5 & 4.5 \
\hline 8.3 & 3.4 \
\hline 7.4 & 5.5 \
\hline 5.4 & 3.3 \
\hline 8.2 & 7.2 \
\hline 8.8 & 4.7 \
\hline 4.5 & 4.1 \
\hline 6.8 & 9.4 \
\hline 7.5 & 5.2 \
\hline 4.8 & 4.4 \
\hline
\end{array}$$ What are the null and alternative hypotheses to test whether there is significant evidence of a different mean adaptation time (in steps) for the two disturbances?

Quizplus · Accepted Answer

The correct hypothesis test for comparing the mean adaptation times between two disturbances in a paired design (since each subject experiences both disturbances) is to test the null hypothesis that the mean difference (Disturbance A - Disturbance B) equals zero against the alternative hypothesis that the mean difference does not equal zero. This accounts for the paired nature of the data and directly tests for a difference in means.

Ten Healthy Adult Subjects Were Asked to Walk on a Treadmill