In Order to Compare the Means of Two Populations, Independent $\begin{array}{ll}\text { Sample 1 } & \text { Sample 2 } \\\bar{x}_{1}=478 & \bar{x}_{2}=481 \\s_{1}=14.2 & s_{2}=11.2\end{array}$

question 46

Essay

In order to compare the means of two populations, independent random samples of 225
observations are selected from each population with the following results. $\begin{array}{ll}\text { Sample 1 } & \text { Sample 2 } \\\bar{x}_{1}=478 & \bar{x}_{2}=481 \\s_{1}=14.2 & s_{2}=11.2\end{array}$

Test the null hypothesis $H _ { 0 } : \left( \mu _ { 1 } - \mu _ { 2 } \right) = 0$ against the alternative hypothesis $H _ { \mathrm { a } } : \left( \mu _ { 1 } - \mu _ { 2 } \right) \neq 0$ using $\alpha = .10$ . Give the significance level, and interpret the result.

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Definitions:

Modern Farming

Modern farming involves the use of advanced technology, machinery, and practices to increase agricultural productivity and efficiency.

Fertilizers

Substances that are added to soil to supply one or more nutrients essential to the growth of plants, available in organic or synthetic forms.

Genetic Varieties

The range of genetic differences within a species, contributing to variations in physical appearance, behavior, and resistance to diseases.

Aquifers

Underground layers of rock or sediment that hold groundwater, which can be extracted using wells.