The framing effect is an example of a cognitive bias, in which the beliefs and preferences of people are influenced by the way a choice is formulated (Tversky & Kahneman, 1981). To investigate this matter, a researcher prepares two versions of the exact same problem:

1. Would you pay $\euro 5$ to participate in a lottery that offers a $10\%$ chance to win $\euro 100$ and a $90\%$ chance to win nothing?
2. Would you accept a gamble that offers a $10\%$ chance to win $\euro95$ and a $90\%$ chance to lose $\euro 5$?

Take note that, in both situations, participants must decide whether to accept an uncertain prospect that will leave them either richer by $\euro95$ or poorer by $\euro 5$.

Out of the $n_1 = 75$ people who were given the first version of the problem, $X_1 = 40$ accepted the offer. Out of the $n_2 = 81$ people who were given the second version of the problem, $X_2 = 36$ accepted the offer.

The researcher suspects that losses evoke stronger negative feelings than costs, and plans on using an independent proportions $Z$-test to determine whether or not people are significantly more willing to accept the first offer than the second, at the $\alpha = 0.01$ level of significance.

State the null and alternative hypothesis of the proposed test.