In Example 1.4, we explored whether voters make decisions based on a candidate’s facial appearance. The researchers described how they had people determine which of two candidates for the U.S. House of Representatives in 2004 had the more competent face. They then looked to see if the one with the more competent face won the election. We will let π = the probability this method predicts the winner.
a. State the appropriate null and alternative hypotheses in the context of this study.
b. Th is method predicted the winner in 189 of the 279 House races that year. Based on these results, what are the values of p̂ and n?
c. Using an appropriate applet, find the p-value using a theory-based test (one-proportion z-test; normal approximation).
d. Summarize your conclusion from your p-value.