16. What is the margin of error, using a 95% confidence level, for estimating the true proportion of adults who self-report that they cannot swim 24 yards? Round to the nearest thousandth.
17. Report the 95% confidence interval for the proportion of adults who self-report that they cannot swim 24 yards. Round final calculations to the nearest tenth of a percent.
18. A survey of 800 randomly selected senior citizens showed that 55% said they planned to watch an upcoming political debate on television. The margin of error for the 95% confidence interval is 3.5 percentage points. Does the confidence interval support the claim that the majority of senior citizens plan to watch the upcoming political debate on television? Explain why or why not.
19. Suppose that you and a friend read the following statement in a news report, “A recent poll found that 54% of voters, give or take 3%, plan to vote for candidate X in the next election (with a confidence level of 95%)”. Your friend then makes the statement, “Hey, look, there’s a 95% chance that somewhere between 51% and 57% of voters plan to vote for candidate X!” How would you explain to your friend why his statement is incorrect, be sure to provide your friend with the correct interpretation of the confidence interval.
20. A polling agency wants to determine the size of the random sample needed to estimate the proportion of voters who favor proposal X. The estimate should have a margin of error no more than 4.5 percentage points at a 95% level of confidence. Determine the minimum size of the sample, rounding to the nearest whole person.