Consider a study investigating whether a recorded phone call is more effective than a flyer in persuading voters to vote for a particular candidate.

The response variable is the proportion of voters planning to vote for the candidate, withpcandpfrepresenting the proportions for the two methods (receiving a phone call and receiving a flyer, respectively.) The sample statistic of interest isp^c-p^f.

We are testingH0:pc=pfvsHa:pc>pf. A randomization distribution of differences in proportion,p^c-p^f, for this test is shown in the figure below.

Interpret the p-value of 0.002 in terms of the probability of the results happening by random chance.

The corresponding statistic value is 0.55.

120 100 80 Frequency 60 40 20 0 0.6 0.4 -0.2 0.0 0.2 0.4 0.6 Difference