An agricultural scientist is investigating the water efficiency of two irrigation methods: Drip Irrigation and Sprinkler Irrigation. The scientist measures the volume of water, in cubic meters per hectare (m3m^3m3), used for a specific crop across several test plots. The results for two independent random samples are summarized in the table below:
\begin{center} \begin{tabular}{|l|c|c|c|} \hline \textbf{Irrigation Method} & \textbf{Sample Size (n)} & \textbf{Mean (\bar{x})} & \textbf{Standard Deviation (s)} \\ \hline Drip (D) & 48 & 215.4 & 18.2 \\ \hline Sprinkler (S) & 52 & 224.8 & 22.5 \\ \hline \end{tabular} \end{center}
By stating your hypotheses clearly, test at the 5% significance level whether there is evidence of a difference in the mean water consumption between the two irrigation methods.
A separate meta-analysis of historical irrigation data is later reviewed. In this analysis, while the Drip method again showed lower consumption, the calculated test statistic for the difference in means was found to be z=−1.42z = -1.42z=−1.42.
A local farmer claims that the Drip method is specifically more efficient, meaning it uses a lower average volume of water than the Sprinkler method.
Test the farmer's claim using the test statistic from the meta-analysis (z=−1.42z = -1.42z=−1.42), stating the hypotheses and the critical value you would use. Conduct this test at the 5% level of significance.
