8. Testing for Differences in Means and Proportions: Independent Proportions Z-test
Independent Proportions Z-test: Test Statistic and p-value
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:
Out of the #n_1 = 47# people who were given the first version of the problem, #X_1 = 22# accepted the offer. Out of the #n_2 = 57# people who were given the second version of the problem, #X_2 = 23# 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 = 0.02# level of significance.
State the null and alternative hypothesis of the proposed test.
- 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?
- Would you accept a gamble that offers a #10\%# chance to win #\euro95# and a #90\%# chance to lose #\euro 5#?
Out of the #n_1 = 47# people who were given the first version of the problem, #X_1 = 22# accepted the offer. Out of the #n_2 = 57# people who were given the second version of the problem, #X_2 = 23# 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 = 0.02# level of significance.
State the null and alternative hypothesis of the proposed test.
#H_0 : \pi_1 - \pi_2\,\,\,\,#
#H_a : \pi_1 - \pi_2\,\,\,\,#
#H_a : \pi_1 - \pi_2\,\,\,\,#
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