Question

A certain forum reported that in a survey of 2001 American adults, 24% 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.)

Answer 1

given data :-

sample size (n ) = 2001

sample proportion () = 24% = 0.24

z critical value for 99% confidence level, both tailed test be:-

a). the 99% confidence interval for the proportion of all adult Americans who believe in astrology :-

interpretation:-

We are 99% confident that this interval contains the true population proportion.

b).margin of error (E) = 0.05

p =0.5 (as we are to calculate irrespective of the value of )

the needed sample size be:-

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