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# Confidence Interval Levels

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I have an opinion poll perfomed on 2 different population sizes, 900 and 10,000 with a 95% confidence level (Confidence Interval details have been computed) for each population.

Opinion Poll

Surveyed 900 Surveyed 10000
Invalid intelligence 52% 468 Invalid Intelligence 52%
Proportion 0.52 Proportion 0.52

Confidence Interval Confidence Interval
Confidence level 95% Confidence level 95%
Standard error 0.017 Standard error 0.005
z-multiple 1.96 z-multiple 1.96
Lower limit 0.49 Lower limit 0.51
Upper limit 0.55 Upper limit 0.53

a) The upper and lower limits from the confidence intervals only deviate from the proportion by 3, suggesting that citizens are indeed in favor of the viewpoint.

b) When using a larger sample size, the standard error is much smaller, as is the difference between the lower and upper limits.
Therefore, this is more even more convincing than the smaller sample size.

c) The question is:
How many people would you have to survey to be 99% confident that you can estimate the fraction of people who believe the US Governement
received invalid intelligence details to fund military operations in the middle east.

##### Solution Summary

Opinion Poll

Surveyed 900 Surveyed 10000
Invalid intelligence 52% 468 Invalid Intelligence 52%
Proportion 0.52 Proportion 0.52

Confidence Interval Confidence Interval
Confidence level 95% Confidence level 95%
Standard error 0.017 Standard error 0.005
z-multiple 1.96 z-multiple 1.96
Lower limit 0.49 Lower limit 0.51
Upper limit 0.55 Upper limit 0.53

a) The upper and lower limits from the confidence intervals only deviate from the proportion by 3, suggesting that citizens are indeed in favor of the viewpoint.

b) When using a larger sample size, the standard error is much smaller, as is the difference between the lower and upper limits.
Therefore, this is more even more convincing than the smaller sample size.

c) The question is:
How many people would you have to survey to be 99% confident that you can estimate the fraction of people who believe the US Governement
received invalid intelligence details to fund military operations in the middle east.

##### Solution Preview

Hello,
The problem, as is stated, needs more detail. In order to determine sample size you need two pieces of data:

- The confidence level you want to establish (which you provide as 99%)

- The margin of error you want the sample proportion to have (which you don't provide)

Thus a valid question here would be: how many people de I need in order to be 99% sure that the observed proportion is within +/-2 percent of the population proportion?

Since you don't specify this margin of error, ...

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