A Gallup Poll of 1800 American adults in February 2009 asked the following question. “Which of the following presidents would you regard as the greatest: Washington, Franklin Roosevelt, Lincoln, Kennedy, or Reagan?” The order of the presidents was rotated to avoid bias. Based on the sample, a 95% confidence interval for the actual proportion American adults who choose Lincoln as the greatest is given by (0.1122, 0.2211).
Which of the following statements are true? Select all the that apply.
Question 7 options:
A 99% confidence interval calculated using the same data will include more plausible values for the actual population proportion. 

If the sample size had been double the sample size in the scenario above, then the 95% confidence interval would be half as wide as the one stated above. 

If a different sample of the same size were to be selected, then there is a 95% chance that the new sample proportion will lie inside the confidence interval stated above. 

If we took several samples of the same size as the scenario given above and constructed 95% confidence intervals for population proportion, then it is reasonable to expect 95% of these confidence intervals to contain the actual population proportion. 

A 90% confidence interval for the population proportion calculated using the same data will be wider than the interval stated above. 

If a different sample of the same size were to be selected and a 95% confidence interval constructed, then there is a 95% chance that the actual population proportion will lie inside the new confidence interval. 
The correct choices among the given ones are:
A 99% confidence interval calculated using the same data will include more plausible values for the actual population proportion.
If we took several samples of the same size as the scenario given above and constructed 95% confidence intervals for population proportion, then it is reasonable to expect 95% of these confidence intervals to contain the actual population proportion.
If a different sample of the same size were to be selected and a 95% confidence interval constructed, then there is a 95% chance that the actual population proportion will lie inside the new confidence interval. 
Hence,
Options A, D and F are correct.
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