When a stream is turbid, it is not completely clear due to suspended solids in the
Chapter 8, Problem 8.2-9(choose chapter or problem)
When a stream is turbid, it is not completely clear due to suspended solids in the water. The higher the turbidity, the less clear is the water. A stream was studied on 26 days, half during dry weather (say, observations of X) and the other half immediately after a significant rainfall (say, observations of Y). Assume that the distributions of X and Y are \(N\left(\mu_{X}, \sigma^{2}\right)\) and \(N\left(\mu_{Y}, \sigma^{2}\right)\), respectively. The following turbidities were recorded in units of NTUs (nephelometric turbidity units):
\(\begin{array}{rrrrrrrr}
x: & 2.9 & 14.9 & 1.0 & 12.6 & 9.4 & 7.6 & 3.6 \\
& 3.1 & 2.7 & 4.8 & 3.4 & 7.1 & 7.2 & \\
y: & 7.8 & 4.2 & 2.4 & 12.9 & 17.3 & 10.4 & 5.9 \\
& 4.9 & 5.1 & 8.4 & 10.8 & 23.4 & 9.7 &
\end{array}\)
(a) Test the null hypothesis \(H_{0}: \mu_{X}=\mu_{Y}\) against \(H_{1}: \mu_{X}<\mu_{Y}\). Give bounds for the p-value and state your conclusion.
(b) Draw box-and-whisker diagrams on the same graph. Does this figure confirm your answer?
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