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A certain forum reported that in a survey of 2002 American adults, 22% said they believed...

A certain forum reported that in a survey of 2002 American adults, 22% said they believed in astrology.

(a)

Calculate a confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology. (Round your answers to three decimal places.)

,

Interpret the resulting interval.

We are 99% confident that the true population mean lies above this interval. We are 99% confident that this interval does not contain the true population mean.     We are 99% confident that the true population mean lies below this interval. We are 99% confident that this interval contains the true population mean.

(b)

What sample size would be required for the width of a 99% CI to be at most 0.05 irrespective of the value of p̂? (Round your answer up to the nearest integer.)

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