# Simulation (2012 #4)

- Author:
- Steve Phelps

A survey organization conducted telephone interviews in December 2008 in which 1,009 randomly selected adults in the United States responded to the following question.

*At the present time, do you think television commercials are an effective way to promote a new product?*Of the 1,009 adults surveyed, 676 responded “yes.” In December 2007, 622 of 1,020 randomly selected adults in the United States had responded “yes” to the same question. Do the data provide convincing evidence that the proportion of adults in the United States who would respond “yes” to the question changed from December 2007 to December 2008 ?*For the simulation, there are two groups (2007 and 2008). We will assume that the 676 people who responded “yes” in 2007 would have responded “yes” regardless of the year. Similarly, will will assume the 622 who responded “yes” in 2008 would have responded “yes” regardless of the year. We have a total of 2,029 adults, with 1,298 of them saying yes. We will randomly sort the 2,029 adults with the 1,298 “yes” respondents into a group of 1,009 another of 1,020. We will then compare the proportion of “yes” respondents in both groups p*_{2008}- p_{2007}and build a distribution. We will then see where our test statistic of 622/1020 - 676/1009 = -0.06 occurs in our distribution. Actually, as a two-tailed test, we will look for test statistic values more extreme than -0.06 or 0.06.