Question 971551: 10. In a poll, 341 out of 775 New York voters surveyed indicated that they approve of the job DeBlasio has done as mayor. Make a 99% confidence interval for the percentage of all New York voters who would approve of DeBlasio’s performance as mayor. Describe the meaning of the interval that you found.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! ph=341/775 = 0.44
SE= sqrt [p(1-p)/n]= 0.01783
z.99 ci= 2.576
z * SE (+/-)= .046
A 99% CI = [0.394, 0.486]
We do not know the true proportion of voters who approve. We are very highly confident that the true value is contained in the interval above.
If we were to perform 100 such tests, 99 of them would contain the parameter. We wouldn't know which 99. We are 99% confident that a majority of voters do not approve of the job. We don't say probable, we say confident.
It's called confidence, because the true value is either in or out of the interval, and that is a dichotomous issue where probability would be 0 or 1.
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