Chapter 8, Problem 36SE

Olympic Viewing A 2018 Gallup poll of 2228 randomly selected U.S. adults found that $39\%$ planned to watch at least a “fair amount” of the 2018 Winter Olympics. In 2014, $46\%$ of U.S. adults reported planning to watch at least a “fair amount.”

a. Does this sample give evidence that the proportion of U.S. adults who planned to watch the 2018 Winter Olympics was less than the proportion who planned to do so in 2014? Use a $0.05$ significance level.

b. After conducting the hypothesis test, a further question one might ask is what proportion of all U.S. adults planned to watch at least a “fair amount” of the 2018 Winter Olympics. Use the sample data to construct a $90\%$ confidence interval for the population proportion. How does your confidence interval support your hypothesis test conclusion?