Effect of Organic Bananas after 25 Days After 25 days, the proportion of fruit flies eating organic bananas still alive is 0.42 , while the proportion still alive eating conventional bananas is 0.40 . The standard error for the difference in proportions is 0.031 .

We find a significant difference in the proportion of fruit flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. We are testing 

\[
\begin{aligned}
& H_{0}: p_{o}=p_{c} \\
& H_{a}: p_{o}>p_{c}
\end{aligned}
\]
where \(p_{o}\) and \(p_{c}\) represent the proportion of fruit flies alive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. In each exercise, show all remaining details of the test, including standardized test statistic, \(\mathrm{p}\)-value from a standard normal distribution, generic conclusion, and an informative conclusion in context. Use a 5\% significance level.