Greatest president ~ A Gallup Poll of 1800 American adults inFebruary 2009 asked the following question. \"Which of the followingpresidents would you regard as the greatest: Washington, FranklinRoosevelt, Lincoln, Kennedy, or Reagan?\" The order of thepresidents was rotated to avoid bias. Based on the sample, a 95%confidence interval for the actual proportion American adults whochoose Lincoln as the greatest is given by (0.1122, 0.2211).Whichof the following statements are true? Select all the thatapply.
A 99% confidence interval calculated using the same data willinclude more plausible values for the actual populationproportion.
If the sample size had been double the sample size in thescenario above, then the 95% confidence interval would be half aswide as the one stated above.
If a different sample of the same size were to be selected, thenthere is a 95% chance that the new sample proportion will lieinside the confidence interval stated above.
If we took several samples of the same size as the scenariogiven above and constructed 95% confidence intervals for populationproportion, then it is reasonable to expect 95% of these confidenceintervals to contain the actual population proportion.
A 90% confidence interval for the population proportioncalculated using the same data will be wider than the intervalstated above.
If a different sample of the same size were to be selected and a95% confidence interval constructed, then there is a 95% chancethat the actual population proportion will lie inside the newconfidence interval.
