Growth spurt: It is generally known that boys grow at an unusually fast rate between the ages of about 12 and 14 . Following are heights, in inches of 10 boys, measured at age 12 and again at age 14 . Can you conclude that the mean increase in height differs from 5 inches? Let \( \mu_{1} \) represent the mean height at age 14 and \( \mu_{d}=\mu_{1}-\mu_{2} \). Use the \( \alpha=0.10 \) level and the \( P \)-value method with the TI-84 Plus calculator.
\begin{tabular}{lllllllllll}
\hline & \multicolumn{10}{c}{ Height } \\
\hline Age 12 & 57.8 & 68.3 & 63.0 & 64.4 & 58.2 & 59.7 & 60.2 & 63.7 & 60.2 & 62.7 \\
\hline Age 14 & 62.8 & 73.6 & 67.7 & 69.2 & 64.6 & 66.1 & 65.9 & 68.3 & 65.2 & 67.9 \\
\hline
\end{tabular}
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Part: \( 0 / 4 \)
Part 1 of 4
(a) State the appropriate null and alternate hypotheses.
\[
\begin{array}{l}
H_{0}: \square \\
H_{1}: \square
\end{array}
\]
This hypothesis test is a (Choose one) \( \square \) test.