In a survey of 2255 adults, 750 say they believe in UFOs. Construct a 99% confid

Question

In a survey of 2255 adults, 750 say they believe in UFOs. Construct a 99% confidence interval for the population proportion of adults who believe in UFOs. A 99% confidence interval for the population proportion is (Round to three decimal places as needed.) Interpret your results. Choose the correct answer below. With 99% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval. The endpoints of the given confidence interval shows that 99% of adults believe in UFOs. With 99% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval. With 99% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.

Explanation / Answer

Here, p = 750/2250 = 0.3333

n = 2250

sigma = sqrt(p*(1-p)/n) = 0.0099

For 99% CI, z critical value = 2.58

lower limit = p - z*sigma = 0.3333 - 2.58*0.0099 = 0.3078

upper limit = p + z*sigma = 0.3333 + 2.58*0.0099 = 0.3588

99% CI for population proportion = (0.3078 , 0.3588)

Interpretation: Option (C)

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