Refer to Exercise 41. The study also estimated that 67% of adults aged 18–29 play video games, but only 25% of adults aged 65 and older play video games.

a. Explain why you do not have enough information to give confidence intervals for these two age groups separately.

b. Do you think a 95% confidence interval for adults aged 18–29 would have a larger or smaller margin of error than the estimate from Exercise 41? Explain your answer.

Exercise 41.

A Pew Research Center report on gamers and gaming estimated that 49% of U.S. adults play video games on a computer, TV, game console, or portable device such as a cell phone. This estimate was based on a random sample of 2001 U.S. adults. Construct and interpret a 95% confidence interval for the proportion of all U.S. adults who play video games.