A "social experiment" conducted by a TV program questioned what people do when they see a very obviously bruised woman getting picked on by her boyfriend. On two different occasions at the same restaurant, the same couple was depicted. In one scenario the woman was dressed "provocatively" and in the other scenario the woman was dressed "conservatively". The table below shows how many restaurant diners were present under each scenario, and whether or not they intervened.
Provocative | Conservative | Total
Yes | 5 | 15 | 20
No | 15 | 10 | 25
Total | 20 | 25 | 45
a) What are the hypotheses? For the purposes of this exercise, you may assume that each observed person at the restaurant behaved independently, though we would want to evaluate this assumption more rigorously if we were reporting these results.
H0: ppr - pcon is equal to 0
HA: ppr - pcon is not equal to 0
b) Calculate the point estimate, the observed difference between the rates of intervention under the provocative and conservative scenarios: pΜpr - pΜcon =
c) Using a standard error of .1491, compute the test statistic.
d) Calculate the p-value. 0.0189
e) Determine the conclusion of the hypothesis test.
We should reject the null hypothesis. The data provide strong evidence that people react differently under the two scenarios.
We should not reject the null hypothesis. The data does not show any significant difference in the way that people react under the two scenarios.