Questions: A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below. Observation 1 2 3 4 5 6 Date 1 / 25 3 / 19 5 / 30 7 / 3 9 / 13 11 / 7 Initial Depth, Xi 45.7 41.7 47.3 45.9 38.2 68.9 Depth Five Years Later, Yi 43.2 40.8 43.4 47.6 33.7 71.0 Determine the test statistic for this hypothesis test. (Round to two decimal places as needed.) Find the P -value for this hypothesis test. P-value = (Round to three decimal places as needed.)
Transcript text: A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below.
\begin{tabular}{lcccccc}
Observation & 1 & 2 & 3 & 4 & 5 & 6 \\
Date & $1 / 25$ & $3 / 19$ & $5 / 30$ & $7 / 3$ & $9 / 13$ & $11 / 7$ \\
Initial Depth, $\mathbf{X}_{\mathbf{i}}$ & 45.7 & 41.7 & 47.3 & 45.9 & 38.2 & 68.9 \\
Depth Five Years Later, $\mathbf{Y}_{\mathbf{i}}$ & 43.2 & 40.8 & 43.4 & 47.6 & 33.7 & 71.0
\end{tabular}
Determine the test statistic for this hypothesis test.
$\square$ (Round to two decimal places as needed.)
Find the P -value for this hypothesis test.
P-value $=\square$ (Round to three decimal places as needed.)
$\square$
Solution
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