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

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.