# True Population

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A marketing firm wants to know the proportion of Sox fans in the Chicago area within a margin of error of 8 percentage points How many people must they survey to be 99% confident that the true population proportion for the Chicago area is within this margin of error? (No prior knowledge regarding proportion is available).

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A marketing firm wants to know the proportion of Sox fans in the Chicago area within a margin of error of 8 percentage points How many people must they survey to be 99% confident that the true population proportion for the Chicago area is within this margin of error? (No prior knowledge regarding proportion is available).

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See attachment please!

Analysis:

The general formula for a confidence interval is

estimate plus/minus (critical value )(standard deviation of the estimate )

A 99% confidence interval for proportions has the form

where N is the sample size and is the sample proportion.

If the population proportion parameter is p, the margin of error, m, for a 99% confidence interval can be calculated using the formula

...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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