In a survey of 2331 adults, 738 say they believe in UFOs. Construct a 90 % confi

Question

In a survey of 2331 adults, 738 say they believe in UFOs. Construct a 90 % confidence interval for the population proportion of adults who believe in UFOs. A 90 % confidence interval for the population proportion is (___,___ ). (Round to three decimal places as needed.) Please show work

Interpret your results. Choose the correct answer below.

A. The endpoints of the given confidence interval shows that 90% of adults believe in UFOs.

B. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

C. With 90% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

D. With 90% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.

Explanation / Answer

n = 738

x = 2331

p^ = x/n = 738/2331 = .3166

Therefore the 90% CI looks like:

.3166 +/- 1.645*sqrt( .3166*.6234 / 2331)

=.3014 to .3317

The correct interpretation is

C is ruled out, as the intrepretation of CI is about population estimate and not sample estimate

D is saying just the opposite ( "Do not beleive") - which is wrong

B is the right interpretation.

A is the not the right interpretation.

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